Pig out having finished tea messily (7)
I believe the answer is:
overeat
'pig out' is the definition.
(synonyms)
'finished tea messily' is the wordplay.
'finished' becomes 'over' (similar in meaning).
'messily' indicates an anagram.
'tea' anagrammed gives 'eat'.
'over'+'eat'='OVEREAT'
'having' acts as a link.
(Other definitions for overeat that I've seen before include "Gorge oneself" , "Take too much food" , "Consume too much food, stuff your stomach" , "Consume excessively" , "Indulge in gluttony" .)