Run from sponsor cornering male in part of theatre (9)
I believe the answer is:
backstage
'part of theatre' is the definition.
(area behind stage)
'run from sponsor cornering male' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'from' is a deletion indicator.
'sponsor' becomes 'backer' (someone backing or sponsoring something).
'cornering' indicates putting letters inside (to corner can mean to trap).
'male' becomes 'stag' (a stag is a male deer).
'backer' with 'r' taken away is 'backe'.
'backe' enclosing 'stag' is 'BACKSTAGE'.
'in' acts as a link.
(Other definitions for backstage that I've seen before include "dressing room area" , "Wings etc" , "Behind the scenes (theatrically)" , "away from public view" , "out of the limelight" .)