Complex sentence: His other important buildings were the Leeds Corn Exchange (1860-3) and the Mechanics' Institute (1860-5), which later became the Civic Theatre and in September 2008 became the new home of the Leeds City Museum.
Split into simpler sentences: His other important buildings in Leeds were the Leeds Corn Exchange (1860-3) and the Mechanics' Institute (1860-5). The latter building later became the Civic Theatre and in September 2008 became the new home of the Leeds City Museum.