Make amends about first of crimes immediately (2,4)
I believe the answer is:
at once
'immediately' is the definition.
(thesaurus)
'make amends about first of crimes' is the wordplay.
'make amends' becomes 'atone' (I've seen this before).
'about' is an insertion indicator.
'first of' suggests taking the first letters.
The initial letter of 'crimes' is 'c'.
'atone' going around 'c' is 'AT ONCE'.
(Other definitions for at once that I've seen before include "This instant, without delay" , "without pause" , "on the spot" , "This instant - no delay (2,4)" , "simultaneously" .)