Coach heads for the undulating hill (5)
I believe the answer is:
tutor
'coach' is the definition.
(I know that coach can be written as tutor)
'heads for the undulating hill' is the wordplay.
'heads for' indicates taking the first letters.
'hill' becomes 'tor' (tor is a kind of hill).
The initial letters of 'the undulating' is 'tu'.
'tu'+'tor'='TUTOR'
(Other definitions for tutor that I've seen before include "Trout (anag)" , "Teach" , "Private or university teacher" , "School" , "Individual teacher" .)