Port uncle drunk getting fat (9)
I believe the answer is:
corpulent
'fat' is the definition.
('corpulent' can be similar in meaning to 'fat')
'port uncle drunk' is the wordplay.
'drunk' indicates anagramming the letters.
'port'+'uncle'='portuncle'
'portuncle' with letters rearranged gives 'CORPULENT'.
'getting' is the link.
(Other definitions for corpulent that I've seen before include "stout" , "Rotund, obese" , "Plump" , "Big" , "Portly" .)