Open-mouthed, Georgia's overwhelmed by primate (5)
I believe the answer is:
agape
'open-mouthed' is the definition.
(I've seen this in another clue)
'georgia's overwhelmed by primate' is the wordplay.
'georgia' becomes 'GA' (abbreviation for the US state).
'overwhelmed by' indicates putting letters inside (inserted letters get absorbed or overwhelmed).
'primate' becomes 'ape' (large primate).
'ga' put within 'ape' is 'AGAPE'.
(Other definitions for agape that I've seen before include "Christian's love" , "showing disbelief" , "love a Christian shows" , "ecclesiastical feast" , "(Of mouth) wide open" .)