Complex sentence: Bass guitarist and vocalist Billy Greer (who had worked with Walsh in the short-lived band Streets after he left Kansas in 1981) completed the lineup, which began rehearsing in July 1985 while Walsh was finishing a tour as sideman for Cheap Trick.
Split into simpler sentences: Bass guitarist and vocalist Billy Greer, who had worked with Walsh in the short-lived band Streets after the singer left Kansas in 1981, completed the lineup. The new Kansas began rehearsing in July 1985, while Walsh was finishing a tour as sideman for Cheap Trick.