Reportedly make too much of having binged (7)
I believe the answer is:
overate
'binged' is the definition.
(binge can mean to overeat)
'reportedly make too much of' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'make too much of' becomes 'overrate' (to make too much of something is to overrate it).
'overrate' is a homophone of 'OVERATE'.
'having' is the link.
(Other definitions for overate that I've seen before include "Binged, glutted" , "Gormandised" , "consumed too much" , "got stuffed" .)