Keen on being at home with set of books around (4)
I believe the answer is:
into
'keen on' is the definition.
(if you're 'into' something you're keen on it)
'at home with set of books around' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'with' is a charade indicator (letters next to each other).
'set of books' becomes 'OT' (abbreviation for the Old Testament).
'around' says the letters should be written in reverse.
'ot' written backwards gives 'to'.
'in'+'to'='INTO'
'being' is the link.
(Other definitions for into that I've seen before include "Taking an active and lively interest (in something)" , "ignition regularly missing" , "Teachers' trade union" , "Involved with" , "To a position within" .)