TEHRAN — At first blush, the election of Donald J. Trump would seem to be bad news for Iran. But there is a chance that on balance, things could work out surprisingly well for the clerics.

Publicly, Iran’s leaders stress that they pay little heed to what happens in the United States, that they pride themselves on their independence. “It makes no difference for Iran who the next U.S. president is,” the supreme leader, Ayatollah Ali Khamenei, said in a speech last week.

Yet he could hardly miss Mr. Trump’s promises on the campaign trail to “tear up” the landmark nuclear agreement reached last year, which he frequently described as the worst deal ever. In response, Ayatollah Khamenei said recently that if Mr. Trump tore it up, “we will set fire to it.”

But Mr. Trump also presents new opportunities for Iran, many analysts say. While he has criticized the nuclear deal, he has also said that the United States should stop backing rebels in Syria and focus on the Islamic State militant group — effectively shifting its support to Iran’s ally in Syria, President Bashar al-Assad.