Competition our chap set up in temporary accommodation (10)
I believe the answer is:
tournament
'competition' is the definition.
(tournament is a kind of competition)
'our chap set up in temporary accommodation' is the wordplay.
'chap' becomes 'man' (I've seen this before).
'set up' is a reversal indicator.
'in' means one lot of letters goes inside another.
'temporary accommodation' becomes 'tent' (I've seen this before).
'man' in reverse letter order is 'nam'.
'our'+'nam'='ournam'
'ournam' going within 'tent' is 'TOURNAMENT'.
(Other definitions for tournament that I've seen before include "series of games" , "Jousting contest" , "Sports contest" , "meeting!" , "open perhaps" .)