Regret being drunk on rum (5)
I believe the answer is:
mourn
'regret' is the definition.
(I've seen this before)
'drunk on rum' is the wordplay.
'drunk' is an anagram indicator.
'on'+'rum'='onrum'
'onrum' anagrammed gives 'MOURN'.
'being' is the link.
(Other definitions for mourn that I've seen before include "Keen" , "Be sad over loss" , "Express sadness" , "Weep for" , "Show sorrow for loss" .)