Look closely at ant, say, circling quietly (7)
I believe the answer is:
inspect
'look closely at' is the definition.
(I've seen this before)
'ant say circling quietly' is the wordplay.
'ant say' becomes 'insect' (ant is a kind of insect).
'circling' indicates putting letters inside (circling can mean going around or containing).
'quietly' becomes 'p' (p for piano and quiet).
'insect' enclosing 'p' is 'INSPECT'.
(Other definitions for inspect that I've seen before include "Look over carefully" , "vet" , "Check" , "Go over" , "Scan" .)