Former D.C. Council chairman Sterling Tucker, who officially left office Jan 2, has begun work as a $182-a-day consultant in fair housing and equal opportunity for the U.S. Department of Housing and Urban Development, a HUD spokesman said yesterday.

Tucker, an unsuccessful candidate for mayor in last fall's elections, has been recommended by HUD Secretary Patricia Roberts to become assistant secretary for fair housing and equal opportunity.

That recommendation was made in October, but has not been acted upon by President Carter, a White House spokesman said yesterday.

Tucker was hired by HUD for a 90-day period beginning Jan. 2, a HUD spokesman said. The spokesman was unable to say if the hiring of Tucker in that capacity was based on an assumption that the 53-year-old former council chairman would be nominated for the post and subsequently confirmed by the Senate, as required.

Harris is a friend and sometimes political ally of Tucker.

As council chairman, Tucker made about $38,000 a year. In his new position, he earns the equivalent of $47,000 a year and works five days a week, the HUD spokesman said.

Tucker is a social worker by training and was for many years executive director of the Washington Urban League. Tucker was unavailable for comment yesterday.