Let off bangers primarily with a crack outside (7)
I believe the answer is:
absolve
'let off' is the definition.
(thesaurus)
'bangers primarily with a crack outside' is the wordplay.
'primarily' suggests taking the first letters.
'with' means one lot of letters go next to another.
'crack' becomes 'solve' (crack can mean to solve or decipher).
'outside' means one lot of letters goes inside another (some letters go outside others).
The first letter of 'bangers' is 'b'.
'a' put next to 'solve' is 'asolve'.
'b' put inside 'asolve' is 'ABSOLVE'.
(Other definitions for absolve that I've seen before include "Clear of blame or guilt" , "Clear of blame or quilt" , "Declare (someone) free of guilt" , "Declare (someone) guilt-free" , "Cleanse" .)