Possibly Grandma in Missouri primarily studying French art (5)
I believe the answer is:
moses
'possibly grandma' is the definition.
(Grandma Moses was an American artist)
'missouri primarily studying french art' is the wordplay.
'missouri' becomes 'mo' (abbreviation for the US state).
'primarily' suggests taking the first letters.
'french art' becomes 'es' ('is' in French - 'art' can mean 'is' eg 'thou art').
The initial letter of 'studying' is 's'.
'mo'+'s'+'es'='MOSES'
'in' acts as a link.
(Other definitions for moses that I've seen before include "He led the Jews from slavery in Egypt" , "Hebrew leader and lawgiver" , "... this OT prophet" , "Prophet found in a basket" , "OT Lawgiver" .)