Glamour industry model whose sins include bush, but no tail (4,8)
I believe the answer is:
show business
'glamour industry' is the definition.
'model whose sins include bush but no tail' is the wordplay.
'model' is an anagram indicator.
'include' means one lot of letters goes inside another.
'but no tail' means to remove the last letter.
'whose'+'sins'='whosesins'
'whosesins' with letters rearranged gives 'showiness'.
'bush' with its final letter taken off is 'bus'.
'showiness' placed around 'bus' is 'SHOW-BUSINESS'.
(Other definitions for show business that I've seen before include "Entertainment industry" , "The world of entertainment" , "Theatre/music industry" .)