Consume rook in the arts arena (7)
I believe the answer is:
theatre
'arts arena' is the definition.
(arena or venue for an arts performance)
'consume rook in the' is the wordplay.
'consume' becomes 'eat' (eating is a kind of consuming).
'rook' becomes 'R' (chess abbreviation).
'in' is an insertion indicator.
'eat'+'r'='eatr'
'eatr' going inside 'the' is 'THEATRE'.
(Other definitions for theatre that I've seen before include "Field of operations" , "Building for drama" , "A tether (anag.)" , "Show" , "Place for dramatic performances" .)