Immediately make amends, bagging century (2,4)
I believe the answer is:
at once
'immediately' is the definition.
(thesaurus)
'make amends bagging century' is the wordplay.
'make amends' becomes 'atone' (I've seen this before).
'bagging' indicates putting letters inside (I've seen this in other clues).
'century' becomes 'c' (common abbreviation).
'atone' enclosing 'c' is 'AT ONCE'.
(Other definitions for at once that I've seen before include "on the spot" , "'Without delay (2,4)'" , "Instantly" , "This instant - no delay (2,4)" , "right away" .)