Beat other outsiders in the open (7)
I believe the answer is:
outdoor
'in the open' is the definition.
(I've seen this before)
'beat other outsiders' is the wordplay.
'beat' becomes 'outdo' (outdoing is a kind of beating).
'outsiders' means to remove the middle letters (only the letters on the outside of the word remain).
'other' with its centre taken out is 'or'.
'outdo'+'or'='OUTDOOR'
(Other definitions for outdoor that I've seen before include "Not inside" , "This sport is not under a roof" , "in the garden, say" , "Located in the open air" , "not under cover" .)