Born in Port Hope, Ontario, Terbenche played junior with the Chicago Black Hawks organization in the nearby town of St. Catharines, Ontario. After one season in the minor leagues Paul made the jump to the NHL in the 1967-68 season, the first season of NHL expansion. However Paul found himself buried in the minors the following two years without even a sniff of NHL action.
Terbenche was claimed by the Buffalo Sabres in the 1970 Expansion Draft. Although he started the year in Buffalo, he ended up playing most of two years with the Salt Lake Golden Eagles of the minor league WHL.
However Paul made a successful return to the NHL starting in 1972-73. For two seasons he became a regular on the Sabres' blueline for two seasons before jumping to the World Hockey Association in 1974.
Paul seemed better suited to play in the WHA. By professional hockey standards Paul was a tiny defenseman, standing just 5'10" and weighing 170 pounds. He had trouble with the physical forwards of the National Hockey League. He was able to find some more success in the less violent WHA. He played with 5 teams over 5 years, including the Winnipeg Jets of 1978-79. That team won the very last Avco Cup as the WHA champion.
The WHA folded in 1979 and it's remaining teams, including the Winnipeg Jets, were merged with the NHL. Terbenche would continue to play hockey for two more seasons but not in the NHL. The Jets traded his rights to the Atlanta Flames. Paul ended up playing two seasons in a former WHA city in Birmingham, this time with the Central Hockey League's Bulls to round out his career.
Paul could be best described as a steady contributor who was hurt by his lack of size. yet he enjoyed a lengthy career which included 189 games in the NHL and 277 in the WHA. All together Paul scored 23 major league goals and 123 points.