The Grumman Aerospace Corp. is combing the ranks of job-seekers here and in two other American cities in search of former Navy pilots willing to train Iranians to fly the F-14 jet fighter.

When the shah of Iran bought 80 Grumman F-14 for $2.2 billion in 1974, he also bought the sophisticated training and maintenance services needed to get the planes in the air and keep them flying.

Grumman delivered on the airplanes, and so far has delivered the teachers and technicians the Iranians need to use the F-14, which when armed with a Phoenix missile is the top weapon in Iran's large and modern air force.

But most of the Grumman employees who have been in Iran since delivery of the F-14 started are coming to the ends of their tours, a Grumman spokesman said yesterday, and the company is hard-pressed to find replacements.

Consequently, job-hunters here, in Norfolk, Va., and in Seattle, Wash., may have seen the ads a Grumman subcontractor has run in newspapers in those cities for the past week.

"Ex-F-14 pilots," the ads proclaim in large type. "Immediate interviews and job offers for out of country openings (Iran) currently being conducted for ex-F-14 pilots. These are long-term assignments with liberal fringes and remuneration."

The ads are not identified as being connected with Grumman. Instead, they ask pilots leaving the Navy to call General Devices, Inc., a Norristown, Pa., firm that has for two years recruited ground maintenance personnel for Grumman to send to Iran.

So far, said John Martin, the General Devices officer whose name appears in the newspapers ads, not a single pilot has responded to his appeal.

Martin said he has no idea why no one has called. Others familiar with the situation have an explanation to offer.

Navy pilots, like pilots from the other services, make their living in the practice of a dangerous art. A lot of steam builds up inside a person encased in a lethal metal tube flying miles off the ground at supersonic speeds. Pilots are renowned for their ingenuity in finding ways to let off that steam.

But Iran, next to Libya, is often identified as the most conservative of the Middle East's Moslem nations. Beyond the country's new urban areas, there are few outlets for good old fashioned: alcoholic America fun, and still fewer when fun involves other appetites.

Grumman has fewer than 10 pilots training Iranian F-14 pilots now, a company spokesman said, and is looking for only about five replacements. The company will not discuss the salaries it proposes to pay.

[According to the Associated Press, General Devices President Ted Raynond said salary for the pilot's has not been set yet, but it probably would be $25,000 a year plus benefits such as housing, schools and medical care. He said there would be a bonus for completing a two-year contract.]

The problem Iran is having with its F-14s is symptomatic of the problems it has with much of the sophisticate weaponry the shah is amassing at a rapid rate.

Iran has had to hire Japanese and Filipinos to drive its trucks. Visitors to Iran often return with stories of planes or trucks or tanks sitting for weeks at docks and in repair yards, waiting for the skilled technicians needed to repair them.

The shah is trying to compress generations of modernization into a few decades. American officials have said, and is using his military, to impart a variety of technical skills to the nation.