Scholarly king backing study (7)
I believe the answer is:
learned
'scholarly' is the definition.
(similar in meaning)
'king backing study' is the wordplay.
'king' becomes 'lear' (King Lear).
'backing' is a reversal indicator.
'study' becomes 'den' (den can mean an office or study).
'den' written backwards gives 'ned'.
'lear'+'ned'='LEARNED'
(Other definitions for learned that I've seen before include "Absorbed information about Leander" , "Knowledgeable - scholarly" , "Discovered, ascertained" , "Having great knowledge" , "Well-educated" .)