Bad live act shunned by clubs that's unusual (7)
I believe the answer is:
offbeat
'unusual' is the definition.
(offbeat means unusual or whacky)
'bad live act shunned by clubs' is the wordplay.
'bad' becomes 'off' (eg meat that's gone off is bad).
'live' becomes 'be' (synonyms).
'shunned by' suggests deleting specific letters.
'clubs' becomes 'c' (abbreviation used in card games such as bridge).
'act' with 'c' taken away is 'at'.
'off'+'be'+'at'='OFFBEAT'
'that's' acts as a link.
(Other definitions for offbeat that I've seen before include "Way-out" , "Kooky" , "Bohemian" , "Unusual or unconventional - perhaps in music" , "Quirky" .)