AFTER FOUR years in the doldrums, the Labor Department seems headed for more lively times. By choosing U.S. Trade Representative William Brock as his new labor secretary -- an appointment almost sure to be confirmed promptly by the Senate -- President Reagan has not only promised the department strong and able leadership; he has also signaled a new interest in how the country's work force is faring and how his policies may affect it.

No appointment by this administration can be expected to win wholehearted approval from organized labor. And Mr. Brock's commendable efforts to reduce international trade barriers have inevitably run up against the protectionist tendencies of many unions. But his record of open and honest dealings on this and other issues hason him solid respect from most labor union leaders. His knowledge of the trade area also puts him in a good position to continue addressing an issue of central importance to future job growth in this country.

Mr. Brock says that job growth and high unemployment among black youth are his first concerns. Those are sensible choices. He also admits that he's "got a lot to learn" about his new department. Some of those lessons won't be pleasant. He will find he has inherited a department from which many of the most able employees have fled. Most of those who remain have been bumped, shoved or demoted from job to job over the last four years. Rebuilding the department's morale and analytical capabilities will also have to be among the new secretary's chief concerns.

There's also the matter of Mr. Brock's successor as chief trade negotiator, a position that will retain its high importance now that the president has formally -- and rightly -- rejected the idea of merging the trade representative's office and the Commerce Department into a single department. The trade representative's job depends crucially on convincing Congress to give him in advance the assurance of enough latitude to negotiate with this country's trading partners. One important reason for Mr. Brock's success in the trade job is that, as a former senator and congressman, he knows and respects Congress. Similar qualifications would be most helpful to his successor.