Beginning with Furuset IF before even turning 16, Skaare had show a great deal of talent at an early age. He joined the Elitserien's Färjestads BK in 1976, only to return to Furuset within a year; the fall of the next season, he signed with the Ottawa 67's of the Ontario Hockey League. Playing with future NHL star Bobby Smith, Skaare scored 12 times and collected 30 assists in 1977-78 - it was good enough to attract the attention of National Hockey League's scouts, and the Detroit Red Wings eventually picked him in the 4th round of the 1978 NHL Entry Draft, 62nd overall.
He was assigned to the Kansas City Red Wings of the Continental Hockey League, where his stellar play earned him a call-up with Detroit. He became the first ever Norwegian to play in the NHL when he made his debuts versus the Colorado Rockies on November 28th 1978. That first NHL game also proved to be his last, as he picked up an injury after being checked by Barry Beck. He would then be reassigned to Kansas City, where he had 8 goals and 26 assists in 37 games. He chose to return in Norway in February 1979.
His comeback with Furuset was a big factor in the team's winning of the Norwegian championship of 1981 and that of 1983. He spent the 1981-82 season with the Klagenfurter AC of the Austrian League and was named the league's best player. He briefly returned to North America in 1984, joining the Tulsa Oilers, but homesickness had him back in his country within a few months.
Skaare was killed in the night of June 21, 1989 in a car accident near Oslo.