Binge, having endless pie - illness follows (3,3)
I believe the answer is:
pig out
'binge' is the definition.
(synonyms)
'endless pie illness follows' is the wordplay.
'endless' means to remove the last letter.
'illness' becomes 'gout' (gout is a kind of health problem).
'follows' says to put letters next to each other.
'pie' with its final letter taken away is 'pi'.
'pi'+'gout'='PIG OUT'
'having' acts as a link.
(Other definitions for pig out that I've seen before include "go on a binge" , "overindulge" , "To eat a lot may" , "gorge" , "Eat too much food" .)