The 1970s era Hawk missiles the Iranians have are probably no longer fit for use, as none of the components, especially the solid rocket fuel, lasts that long. But assume the Iranians have managed to keep these missiles working via smuggled, or home made, parts. The Hawk is a 17 foot long, 1,300 pound missile, with a range (when fired from the ground) of some 40 kilometers. Fired in air-to-air mode, it could go 100 kilometers or more.
Hmmm, now that's interesting. Consider that the F-14 was designed to fire the Phoenix missile, which was 13 feet long, weighed 1,000 pounds and had a range of nearly 200 kilometers. None of the Phoenix missiles Iran had in the late 1970s, are believed to be still operational. Indeed, the U.S. technicians who were maintaining the Iranian missiles, apparently disabled them before they left the country. The new Iranian government never got their Phoenix missiles working, although they claim they did, and claim to have built their own copies of the Phoenix. These mythical missiles have never been used in a confirmed combat situation, even during the 1980s Iran-Iraq war.
Both the Hawk and Phoenix have the same type of guidance system (semi-active radar homing.) Basically, the missile homes in on the radar signals, from a ground or airborne radar, bouncing off the target. So, in theory, the Iranians could have modified Iranian made Hawks to use the F-14 radar. In theory. As a practical matter, the Iranians have a long history of making unproven claims of how they have kept old U.S. equipment in working order. The Iranians also regularly claim to have built modern weapons that are never seen in action, or offered for export sale. In other words, this use of the Hawk as an air-to-air missile appears to be more of this Iranian hype.
Iran claims to have modified Hawk anti-aircraft missiles to be fired from F-14 aircraft, as an air-to-air missile. In theory it's possible, but practicality is another matter.