Left the fathead out, as permitted (3)
I believe the answer is:
let
'permitted' is the definition.
(to let something happen is to permit it)
'left the fathead out' is the wordplay.
'the fathead' becomes 'f' (head letter of 'fat').
'out' suggests deleting specific letters.
'left' with 'f' taken away is 'LET'.
'as' acts as a link.
(Other definitions for let that I've seen before include "Disappoint or fail to support - ... down" , "Allow; tennis fault" , "Permit; lease" , "Permit or rent" , "Permitted" .)