Putin and Rouhani

Trump may pursue a reset with Russia but take a hard line on Iran. If so Moscow will not betray its newfound partnership with Tehran

Trump said he would give improving Russia relations a shot but was hardline on Iran throughout the campaign (albeit being careful not to commit himself to tearing up the nuclear deal).

Is he going to pursue a warming with Russia, while ratcheting up hostility towards Iran? If so will he try to convince Moscow to join him? It's possible.

If he does will Moscow forsake Tehran for Trump? Absolutely not.

The ties between the two nations shunned by the west have become too deep to throw away now.

Russia and Iran are obviously allies in Syria. Russia also wants to induce Iran into the Shanghai Cooperation Organization which would go a long way towards breaking Tehran's international isolation.

Next there is the equally important economic aspect. The two nations have cultivated a number of commercial links, whether it is Iranians exporting fish and vegetables or Russians selling arms and technology. But as befits two energy giants the two meat and bone of the economic relationship are energy deals, a number of them were signed just last week:
A Russian delegation to Tehran signed nine agreements in industries ranging from energy to railways. Gazprom reached an unspecified accord with Iran's state natural gas company, and its subsidiary, Gazprom Neft PJSC, signed a deal to study the Cheshmeh-Khosh and Changuleh oil fields. State-run Gazprom is the third Russian energy company to sign a memorandum of understanding with Iran, joining Lukoil PJSC and Zarubezhneft OAO.

"Our priority is to develop Iran's big projects," Novak said at one of several signing ceremonies on Tuesday. "These agreements will have a significant influence on the relationship between our two countries."

Russia also signed agreements to develop the Bandar Abbas power station on the southern Iranian coast and to electrify a railway in the country's northeast, Iran's Information and Communications Technology Minister Mahmoud Vaezi said. Together with other agreements in trade, finance, industry, mining and agriculture, the preliminary deals could lead to final contracts with a total value of $10 billion, he said.
Moreover the two countries are powering on with the scheme to use their national currencies rather than the dollar in their mutual trade:
Vaezi [Iranian minister and chair of the Russia-Iran Trade Comission] said both sides have reached an agreement on the simultaneous opening of branches of their local banks in Iran and Russia to remove the obstacles faced in bilateral trade. Highlighting that the said talks between Iran and Russia focused primarily on the use of local currency in mutual trade,

Vaezi said Iran and Russia have agreed to use rials and rubles, respectively, rather than U.S. dollars in bilateral trade, pointing out that negotiations between both the Russian and Iranian central banks will commence soon.
What this means is that the two countries are insulating their expanding economic relationship from the effects of sanctions, particularly any increased sanctions Trump administration may have in store for Tehran.

If US in 2017 pursues a reset with Russia but insists the price is for Russia to forsake its partnership with Iran then that is a deal that Moscow won't take.