Excuse given by a bishop on crack (7)
I believe the answer is:
absolve
'excuse' is the definition.
(I've seen this before)
'a bishop on crack' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'on' is a charade indicator (letters next to each other).
'crack' becomes 'solve' (crack can mean to solve or decipher).
'a'+'b'+'solve'='ABSOLVE'
'given by' acts as a link.
(Other definitions for absolve that I've seen before include "Declare (someone) free of guilt" , "Exculpate" , "Acquit - free of blame" , "Grant remission of sins" , "Set free from guilt" .)