PRESIDENT CARTER was well advised to choose former Gov. Reuben Askew of Florida as his special trade representative.Mr. Askew was courageous to accept.

A lot of people know more about trade than Mr. Askew does. But the job requires expertise less than the political standing (and stamina) to keep forcing difficult decisions. International trade policy always involves jobs, profits and the collision of one economic interest with another. Mr. Askew joins the administration at a moment when it is mainly preoccupied by a recession and a difficult reelection campaign - circumstances not generally conducive to enlightened and far-sighted attitudes toward foreign trade.

In the period when Robert S. Strauss held the office, the main job of the president's special trade representative was the enactment of a Trade Act embodying five years of worldwide negotiations. With its passage late last month, Mr. Strauss left for the Middle East. There is not likely to be any similar public triumph for his successor. But as he puts the new law into operation, he will set precedents that will quietly guide American practice for years to come.

Trade administration is now to be reorganized, with the idea of retaining the policy and the international negotiations at the White House. The work of reporting and analysis is to go to an augmented Department of Commerce or, as it will be more grandly known, the Department of Trade and Commerce. While that division of labor sounds simple, Mr. Askew will find it to require careful watching. It is a reliable rule that the lower the level at which trade matters are decided, the narrower and more special the interests served. The protectionist lobbies wanted to get trade out of the White House altogether. After all those promises to cut the White House staff, Mr. Carter, is uneasy about any large reinforcement of the trade office there. Mr. Askew is going to have to push hard for enough of a staff to ensure effective control over his responsibilities.

The new trade law establishes a series of codes that state general principles for resolving the perennial quarrels over sugsidies, product standards and so forth. But the worth of these codes depends wholly on the specific agreements still to be negotiated under them - and these negotiations are now Mr. Askew's job. The process, most of the time, is silent, invisible and incomprehensible to all but the lobbyists. It will fall to Mr. Askew from time to time to remind everyone - Congress and the public, not to mention Mr. Carter - of the broad national interests at stake.

It's hard, abrasive work and not a great deal of fun. You can easily say only one thing for it: More than most of the jobs at this or any White House, its success or failure will influence future trade balances, the dollar's value, and, in turn, the country's standard of living.