Complex sentence: The band performed its first gig from the back of a lorry at the Campaign for Nuclear Disarmament Rally in Elder Park, and went on to be a local success, playing gigs at the Mars Bar in Glasgow.
Split into simpler sentences: The band performed its first gig from the back of a lorry at the Campaign for Nuclear Disarmament Rally in Elder Park. It was a local success, playing gigs at the Mars Bar in Glasgow.