Complex sentence: McNair was part of a quartet Mingus formed to rehearse with during his stay in Britain, but the band never played live in front of a paying audience thanks to the UK Musicians Union's ban on US musicans in British nightclubs.
Split into simpler sentences: McNair was part of a quartet Mingus formed to rehearse with during his stay in Britain. Unfortunately, the band never played live in front of a paying audience, due to a ban imposed by the UK Musicians' Union on US musicans in British nightclubs.