Peter Bergen is CNN's national security analyst, a vice president at New America and a professor of practice at Arizona State University. He is the author of " United States of Jihad: Investigating America's Homegrown Terrorists ."

(CNN) President-elect Donald Trump has a host of national security challenges to deal with as he assumes office, from the resurgence of the Taliban in Afghanistan, to the grinding Syrian civil war, to the flexing of Russian muscles under President Vladimir Putin, to how to deal with ISIS as the terrorist army retreats in Iraq.

These are all-important problems, none of which have easy answers and whatever the United States does or doesn't do about them entails risks.

During the campaign, Trump in many ways repudiated President Obama's national security and foreign policy approach on issues like the Iran nuclear deal and immigration. So there's a real question of continuity or disruption with Trump, which wouldn't have existed if Clinton was president-elect. That said, the national security challenges facing the nation are the same today as they were yesterday.

President Obama's approach to these challenges, which he has summarized as "don't do stupid s---" certainly seems fair enough when you consider that the United States is still involved in the war in Iraq 13 years after it overthrew Saddam Hussein, but botched what came after the Iraqi dictator's overthrow.

Inaction also comes with its own downsides: Consider the Syrian civil war that the United States has largely sat out on the sidelines, and which over the past five years has turned into one of the worst humanitarian crises since World War II. Those consequences will be a major problem for the new president.

Here are some ideas about what to do about four of the most significant foreign policy and national security issues that President Trump will face.

1. Afghanistan: The longest war

America's longest war was mentioned only once in passing during the three presidential debates between Hillary Clinton and Trump, yet it is arguably the foreign policy issue that needs the quickest attention.

No matter how you spin it, the Taliban are now doing relatively well in Afghanistan. They are in control or they are contesting control of around a third of the Afghan population, a total of some 10 million Afghans, according to U.S military officials.

Few but the Taliban want to see a repeat in Afghanistan of what happened in Iraq after the withdrawal of US troops there at the end of 2011. Within three years of that withdrawal, ISIS was able to seize vast swaths of the country.

The Obama administration had planned to end the US troop presence in Afghanistan, but given how the Taliban have surged back, officials decided not to go lower than 8,400 soldiers by the beginning of 2017. This force is just sufficient to maintain key American bases such as Bagram Air Base outside of Kabul.

NATO recently pledged to keep supporting the Afghan army to the tune of $15 billion over the next four years. Trump should add to that pledge by committing the United States to remain in Afghanistan until the Taliban threat to the central government is long over.

A plan to roll back the Taliban to the point where they don't threaten the stability of country would involve significant numbers of U.S. Special Forces to train and advise the Afghan army, as well as American intelligence assets and air support deployed to support it.

Trump should point to the Strategic Partnership Agreement that the United States has already negotiated with the Afghan government. It provides the framework for a long-term American presence until at least 2024.

It would be a huge mistake for Trump, who is after all a New Yorker, to forget the lesson of 9/11, when Osama bin Laden's al Qaeda, sheltered by the Taliban regime in Afghanistan, was able to plan and execute the terrorist attacks that killed almost 3,000 Americans.

2. After ISIS

The fall of Mosul, ISIS' Iraqi capital in Iraq and the second largest city in Iraq is likely only weeks away. Next up is ISIS' capital in Syria, Raqqa, which will likely fall some time next year. These, of course, are hopeful developments for Iraq, Syria and the world at large, but they come freighted with two problems.

The first is what happens to the "foreign fighters" from around the Muslim world who have flocked to fight with ISIS, numbering some 40,000 militants, including around 7,000 Europeans. Not all these foreign fighters will be captured or killed on the battlefield and the United States must work closely with Turkey and other regional allies to ensure these fighters do not return to their home countries to foment additional terrorism.

The bigger issue, however is that ISIS is not itself the fundamental problem that ails the Middle East, but rather it's a symptom of deeper problems that the Trump administration must do its best to ameliorate. They are the deepening Shia-Sunni rivalry across the region that is stoked by Iran and the Gulf states; the collapse of governance in states around the Arab world, and the massive outflow of refugees to the West that are a result of the first two problems.

The deep problems that afflict the Middle East are not easy to fix, but they must be dealt with if we are not to see a son of ISIS, or even a grandson of ISIS developing in the years to come.

3. Wading into Syria's civil war

Trump has long said he favors a " safe zone " in Syria to prevent Basher al Assad's regime from carrying out indiscriminate airstrikes against Syrian civilians and to halt the refugee flow out of Syria.

This is an excellent idea in theory, but, based on multiple discussions with US military officials based in the Middle East last week, implementing such a safe zone would be quite complex because it would entail a no-fly zone if it had a chance to succeed.

First, appropriate authorities would have to be given to American fighter jet pilots to shoot down planes defying the no-fly zone, including possibly Russian planes that are also conducting airstrikes in Syria.

Second, complicating matters, some of the planes that the Syrian air force flies are the same model as some of the older Russian planes that are flying over Syria.

Third, Syria has excellent air defenses that would have to be taken out. The Russians have deployed the SA-23 surface-to-air missile system to Syria, which, according to US military officials, is one of the most sophisticated air defense systems in the world.

Fourth, as a matter of international law a no-fly zone in Syria would require some kind of UN resolution authorizing it and Russia would veto such a measure.

In 1999, NATO did impose a no-fly zone in Kosovo without seeking a UN resolution, in order to carry out air strikes on Serbian forces. Trump could do something similar, for instance, unilaterally ordering American warplanes to bomb Syrian airfields so Assad's warplanes could no longer use them. Of course, this would be a significant escalation of America's role in the conflict and would also skirt international law.

Debates in the States about whether to intervene or not in the Middle East tend to be black and white. Intervention gave us the Iraq war fiasco in 2003 and so many Americans believe that the United States shouldn't intervene in the Arab world again in any significant way. Indeed, during the campaign Trump often aligned himself with an isolationist American foreign policy, saying in August "President Obama and Hillary Clinton should have never attempted to build a democracy in Libya, to push for immediate regime change in Syria or to support the overthrow of Mubarak in Egypt.."

But the fact is that there are also costs to inaction as well as to action and the past five years of the Syrian civil war has resulted in some 12 million external and internal Syrian refugees, almost half a million deaths and the rise of ISIS.

Trump should certainly consider policies that go beyond the present narrow Obama administration policy of only fighting against ISIS in Syria, and among those policy options he should consider bombing Assad's air fields

4.No fly, no buy

Trump should push to ensure that the 81,000 people who are on the U.S. "no-fly" list of suspected terrorists are not allowed to buy weapons in the States.

Omar Mateen, who carried out the Orlando massacre this year killing 49 people and Nidal Hasan who killed 13 at Fort Hood Texas in 2009 were both FBI subjects of interest.

Yet they legally purchased semi-automatic weapons before they carried out their mass murders. In the future, such purchases of weapons must, at a minimum, be flagged to law enforcement or, even better, simply barred.

Indeed, Trump at the first presidential debate in September said, "We have to look very strongly at no-fly lists. ... I tend to agree with that," implying h e is in favor of some kind of tightening up on the ability of suspected terrorists to buy guns.

The NRA may object that some Americans who are on the no-fly list shouldn't be on it, but this is a massive red herring. In June, US Sen. Dianne Feinstein (D-Calif.) revealed that fewer than a thousand of the 81,000 on the no-fly list are Americans.

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Only the most extreme gun rights advocates can seriously claim that the Second Amendment rights of a handful of Americans suspected of being terrorists outweighs the right to live for the dozens of Americans who have been killed by terrorists in the United States who legally purchased military-style weapons before they carried out their attacks.