The Cincinnati Reds yesterday signed outfielder Dave Parker to a three-year contract extension, carrying through the 1988 season, with an option for 1989.

Parker, 33, was the Reds' first major free-agent acquisition. He left the Pittsburgh Pirates after 11 major league seasons, returning to his home town last season under a two-year contract that reportedly pays him $800,000 a year.

Last year, the right fielder hit .285 with 16 home runs and 94 runs batted in . . .

Jim Palmer, retired pitching star of the Baltimore Orioles, has signed to do commentary on Home Team Sports' telecasts of Orioles games in 1985.

Palmer, who has remained in the public eye as a model for Jockey underwear and a baseball analyst for ABC-TV, will tailor his new assignment to fit his duties with ABC. He is expected to work about one-third of the 82 regular-season games on the HTS schedule.

"After working with (Howard) Cosell," Palmer said, "it will be a pleasure working here." . . .

Tug McGraw, a relief pitcher and leader with the world champion 1969 New York Mets and 1980 Philadelphia Phillies, retired after 19 major league seasons. A master of the screwball pitch, his career record was 96-92 with 179 saves . . .

Designated hitter Don Baylor of the New York Yankees, the national sports chairman for Cystic Fibrosis, was named the winner of major league baseball's Roberto Clemente Award, which honors the player who best exemplifies the game . . .

Oakland A's pitcher Mike Norris, stopped by the California Highway Patrol just south of Oakland because, police said, he was driving at 75 mph, was arrested and held for investigation of driving under the combined influence of alcohol and drugs, resisting arrest, and possession of a quarter-gram of cocaine. He also was cited for possession of less than an ounce of marijuana . . .

This year's Cracker Jack Old Timers Baseball Classic, scheduled for July 1 at RFK Stadium, will feature Harvey Kuenn (American League) and Birdie Tebbetts (National League) as managers.