Combined Institute backed by nobody (2,3)
I believe the answer is:
in one
'combined' is the definition.
(as in 'all in one')
'institute backed by nobody' is the wordplay.
'institute' becomes 'i' (common abbreviation as in MIT).
'backed by' means one lot of letters go next to another.
'nobody' becomes 'none' (not a single person).
'i'+'none'='IN ONE'
(Other definitions for in one that I've seen before include "A hole . . . . . is a singular golf score" , "united" , "As a single unit" , "Combined" .)