Although hearings on her nomination as secretary of labor have not even been scheduled, Lynn Martin has already made her first appointment.

Deputy Labor Secretary Rod DeArment said yesterday that he had agreed to stay on in the department's No. 2 post after a meeting Tuesday with Martin. Sources said Martin offered DeArment the job after clearing it with the White House.

DeArment's decision resolves a major concern in the White House and the Labor Department that Martin's deputy possess some expertise on labor matters. Prior to Martin's selection of DeArment, the White House interviewed at least two people for the deputy's job, sources said.

When Elizabeth Hanford Dole announced in late October that she was resigning to become president of the American Red Cross, it was expected that DeArment would return to private law practice after a suitable transition period with Dole's successor.

But after Tuesday's meeting, DeArment said he was impressed with Martin and excited about staying on and working for her.

His decision also goes a long way toward getting Martin off to a good start with organized labor. Although labor has reacted coolly to the selection of Martin, a five-term Republican House member from Illinois who was defeated in her bid to unseat Sen. Paul Simon (D-Ill.), the AFL-CIO has developed a good relationship with DeArment.