Study steadfast support (7)
I believe the answer is:
confirm
'support' is the definition.
('confirm' can be a synonym of 'support')
'study steadfast' is the wordplay.
'study' becomes 'con' (I've seen this before).
'steadfast' becomes 'firm' ('firm' can be a synonym of 'steadfast').
'con'+'firm'='CONFIRM'
(Other definitions for confirm that I've seen before include "Make (provisional arrangement) definite" , "Establish the truth of" , "Substantiate" , "Provide support for the truth" , "Provide supporting evidence, make definite" .)