Satisfied, peer around, having permit (7)
I believe the answer is:
replete
'satisfied' is the definition.
(I've seen this before)
'peer around having permit' is the wordplay.
'around' indicates an anagram.
'having' is an insertion indicator.
'permit' becomes 'let' (synonyms).
'peer' is an anagram of 'repe'.
'repe' placed around 'let' is 'REPLETE'.
(Other definitions for replete that I've seen before include "Full, satiated" , "Stuffed, gorged, sated" , "Filled to satisfaction" , "Full - pet leer (anag)" , "Gorged, satiated" .)