Confess, having received unfriendly rebuke (8)
I believe the answer is:
scolding
'rebuke' is the definition.
(scolding is a kind of rebuke)
'confess having received unfriendly' is the wordplay.
'confess' becomes 'sing' (I've seen this before).
'having received' indicates putting letters inside.
'unfriendly' becomes 'cold' (similar in meaning).
'sing' enclosing 'cold' is 'SCOLDING'.
(Other definitions for scolding that I've seen before include "lecture" , "telling-off" , "Rebuking, berating" .)