Punishment I had - and quick! (5)
I believe the answer is:
rapid
'quick' is the definition.
(synonyms)
'punishment i had' is the wordplay.
'punishment' becomes 'rap' (as in taking the rap for something).
'i had' becomes 'i'd' (I'd).
'rap'+'id'='RAPID'
'and' is the link.
(Other definitions for rapid that I've seen before include "Happening quickly" , "Swift, speedy" , "Expeditious" , "Fast, quick" , "Speedy, quick" .)