Complex sentence: The Fighting Irish lasted only two years in the new CCHA, after designating Ice Hockey as a club sport for the 1983--1984 season the team played in the Central States Collegiate Hockey League (CSCHL).
Split into simpler sentences: The Fighting Irish lasted only two years in the new CCHA, when ice hockey was downgraded to a club sport for the 1983--1984 season. During that season, the Fighting Irish played in the Central States Collegiate Hockey League (CSCHL).