Simmons abandoned Kiss, heading off with British rock band (7)
I believe the answer is:
genesis
'british rock band' is the definition.
(British band)
'simmons abandoned kiss heading off' is the wordplay.
'simmons' becomes 'Gene' (Kiss musician Gene Simmons).
'abandoned' is an anagram indicator.
'heading off' means to remove the first letter.
'kiss' with its first letter taken away is 'iss'.
'iss' with letters rearranged gives 'sis'.
'gene'+'sis'='GENESIS'
'with' acts as a link.
(Other definitions for genesis that I've seen before include "Origin or formation of something" , "Origin (of the Old Testament?)" , "the start of something" , "OT opening" , "rock band" .)