Mary Hart has been the host of “Entertainment Tonight” since l982. But her contract is up this year, and insiders are speculating that the plum job could be offered to Lara Spencer, who anchors syndicated sister show “The Insider.” Spencer commuted from Greenwich, Conn., when “The Insider” was shot at a Times Square studio, but the show recently moved to Los Angeles, where “ET” is also produced. She conven iently now lives in Beverly Hills with her husband, former CNN reporter David Haffenreffer. Our source says Spencer wants the job badly. “There are no plans to make host changes to ‘Entertainment Tonight,’ ” said Lisa Sum mers Haas, a rep for both “ET” and “The Insider.”