SAN JOSE — The first big test of presumptive Mayor-elect Sam Liccardo’s leadership is already upon him, as he moves to ease the rancor between City Hall and the police union that opposed him.

No one expects Liccardo — a staunch backer of outgoing Mayor Chuck Reed’s pension reforms that he says saved the city from insolvency — or the officers who blame those same reforms for driving cops off the force, to back off their positions. But many see the pending change of leadership at both City Hall and the police union as the best opportunity to reset the conversation.

“Now that the election is over, I think we have all the space to recognize we have too much in common to be fighting the battles of the past,” Liccardo said.

Officer James Gonzales, incoming vice president of the San Jose Police Officers’ Association, signaled that the task won’t be easy.

“It’s not going to change unless dramatic things are done,” he said. “Immediately, if not sooner.”

Liccardo took the first step toward easing tensions by leading the City Council in a unanimous vote Friday not to investigate the police union for allegedly undermining recruitment efforts as part of a political campaign against the city.

That charge, which the union denies, arose with a former recruit’s published claim that the police union chief urged cadets to quit to bolster their case that pension reforms were decimating the police force, and that recruiters were quick to reject her for failing a firearm safety test instead of retraining her. Surfacing just before Tuesday’s election, it was the latest flashpoint in an ongoing war between rank-and-file cops and city leaders.

Friday’s council vote, Liccardo said, was an olive branch from him and his allies to their biggest political foe. But for the union, the move only confirmed suspicions that it was driven by politics.

“It’s clear to everybody that it was a political stunt, and now that the election is over, this thing is dead,” said Sgt. Jim Unland, the outgoing union president.

But even Reed acknowledged the changing of the guard offers Liccardo a fleeting chance to mend fences.

“It’s certainly an opportunity that Mayor-elect Liccardo will try to take advantage of to reset the relationship, and get everyone focused on trying to solve the problems we have,” Reed said. “Not that we necessarily agree on everything, but there are certainly some problems that we agree upon, so why not focus on trying to solve those problems?”

Liccardo has also dangled some ideas that may win some support among officers, such as trying to give away bilingual pay increases and letting retirement-age cops work part time while collecting a piece of their pensions.

Unland, however, doubted a change in tone would be enough to mollify the rank and file’s concerns.

“It’s not to say there weren’t personality issues complicating things, and I’m a dance partner in that,” said Unland, who plans to retire in January. “But taking personality issues out of equation, you still have a policy driving people away and making it difficult to recruit.”

While the police union denies urging recruits to quit, it has acknowledged relaying concerns about the city’s pay and benefits and in one instance hosted outside recruiters looking to hire existing officers.

Liccardo is holding firm on the existing efforts to control retirement costs for city employees, saying Reed “saved this city from fiscal calamity.” But he noted the new union leadership knows it doesn’t have “the same emotional baggage” as its predecessors and can forge new paths.

“I say that not to point fingers,” Liccardo said. “But we’ve been through a very tumultuous political battle and we know wounds result from that. And having new leadership, I think, has helped on the union side because I think there is an ability to think and look at things with a fresh perspective.”

Gonzales will be part of that new union leadership, along with Sgt. Paul Kelly, expected to step in Jan. 1 as president. Gonzales said the closeness of the mayoral race would signal to city leaders that residents want them to soften their stance toward police.

“Our goals are to restore the Police Department and make our citizens feel safe in their neighborhoods again, and that comes from having a police department that is competitive, where people want to come work here and stay,” Gonzales said. “With the mayor’s race coming down the middle, we’re divided. The tone that has changed was from our citizens, not from leaders of either side. That’s where the pressure is going to come from to repair a broken police department and divided city.”

As it stands, the department has just over 1,000 sworn officers, down from 1,400 six years ago, and the past few police academies have been modest to anemic in terms of numbers. For the past three years, at least 100 officers annually have gone out the door by either retiring, some early, or taking jobs elsewhere, outpacing the number joining the ranks by nearly 2-to-1.

Another Bay Area city could be a harbinger for San Jose if the tenor of the discussion remains on its existing path. In Vallejo, retirement costs for cops and other public employees helped drive the city into bankruptcy in 2008, and the rancor between city leaders and police remains deep. City finances remain strained by rising retirement costs, and its plan for exiting bankruptcy has left a depleted and demoralized workforce.

But San Jose is in better financial shape. And Liccardo points to an 11 percent pay restoration as an example of gains that can be made while the sides and courts wrangle over voter-approved pension reforms.

“We have a strong incentive to work together to address outstanding concerns over disability and pay that I believe can go a long way to addressing the frustrations of many of our officers,” he said.

Contact Robert Salonga at rsalonga@mercurynews.com. Contact Mike Rosenberg at mrosenberg@mercurynews.com.