Klima played two years with CHZ Litvinov of the country's first division. He scored 36 points in 44 games in 1982-83 then moved up to Dukla Jihlava where he starred for two years. Klima was chosen 88th overall by the Detroit Red Wings in the 1983 Entry Draft. The gifted forward played for Czechoslovakia at the World Junior Championships winning silver in 1983 and bronze in 1984. He also scored three points in five games for his country at the 1984 Canada Cup. He scored 45 points in 35 games for his club team in 1984-85 before escaping to the West.

Klima scored 32 goals as a rookie in 1985-86 and consistently produced at this pace in his first four years although he was capable of doing better. The high point of his Detroit tenure was scoring ten goals while helping the club reach the semifinals in 1988. This output broke the old mark set by Gordie Howe in 1955 and equaled by "number 9" in 1964.

Klima was traded to the Edmonton Oilers with Joe Murphy and Adam Graves in the deal that brought sniper Jimmy Carson home to Detroit. Klima scored 25 goals in 63 games then five goals in playoffs while helping Edmonton win the Stanley Cup. His biggest moment came on the first night of the championship series in Boston when he scored at 55:13 of overtime in the longest game game in the history of the finals.

The talented sniper scored a personal-best 40 goals in 70 games in 1990-91. Overall he produced 118 goals in just under four seasons in Alberta. Klima was traded to the Tampa Bay Lightning in 1993 and scored 28 goals his first year but his production slipped over next two seasons. He played 33 games in 1996-97 with L.A., Pittsburgh, and Edmonton but only scored two goals. In 1997-98 Klima played with Krefeld Pinguine in Germany then signed as a free agent with Detroit in January 1999. He scored one goal in 13 games in his NHL swan song.