Greyhound, maybe, in care of a church (5)
I believe the answer is:
coach
'greyhound maybe' is the definition.
(Greyhound is a coach service)
'care of a church' is the wordplay.
'care of' becomes 'co' (c/o can mean 'care of' when addressing mail).
'church' becomes 'ch' (common abbreviation).
'co'+'a'+'ch'='COACH'
'in' acts as a link.
(Other definitions for coach that I've seen before include "Stage" , "Trainer and bus" , "Train - or part of one!" , "Instruct" , "Trainer as of soccer team" .)