Worry rook gets into the arts arena (7)
I believe the answer is:
theatre
'arts arena' is the definition.
(arena or venue for an arts performance)
'worry rook gets into the' is the wordplay.
'worry' becomes 'eat' (something worrying may eat someone up).
'rook' becomes 'R' (chess abbreviation).
'gets into' indicates putting letters inside.
'eat'+'r'='eatr'
'eatr' inserted inside 'the' is 'THEATRE'.
(Other definitions for theatre that I've seen before include "Operating area" , "Place for operation or play" , "Major area of military activity" , "Eg, Oxford's Sheldonian" , "Playhouse or sphere of action" .)