Local team in tears, mostly (8)
I believe the answer is:
resident
'local' is the definition.
(a resident of a particular area)
'team in tears mostly' is the wordplay.
'team' becomes 'side' (both can mean a sports team).
'in' is an insertion indicator.
'tears' becomes 'rents' (rent can mean a tear or gap).
'mostly' means to remove the last letter (most but not all of the word).
'rents' with its last letter taken off is 'rent'.
'side' going within 'rent' is 'RESIDENT'.
(Other definitions for resident that I've seen before include "Permanent dweller" , "always in memory" , "One living in the place referred to" , "Dwelling in a place for some time" , "One living somewhere" .)