Overfill with teas, perhaps (4)
I believe the answer is:
sate
'overfill' is the definition.
(I've seen this before)
'teas perhaps' is the wordplay.
'perhaps' is an anagram indicator.
'teas' anagrammed gives 'SATE'.
'with' acts as a link.
(Other definitions for sate that I've seen before include "Satisfy more than fully" , "Malaysian dish" , "Satisfy to excess" , "Glut" , "cloy" .)