Trainer (5)
(Other definitions for tutor that I've seen before include "Private or university teacher" , "Personal teacher" , "Trout (anag)" , "School" , "Teacher (often private)" .)
'trainer' is the definition.
(coach is a kind of trainer)
This is all the clue.
(Other definitions for coach that I've seen before include "Trainer and train carriage" , "Type of bus" , "Trainer as of soccer team" , "Stage" , "Sports or lifestyle trainer" .)