Tutor's initial career suggestion (5)
I believe the answer is:
trace
'suggestion' is the definition.
(I know that suggestion can be written as trace)
'tutor's initial career' is the wordplay.
'initial' suggests taking the first letters.
'career' becomes 'race' (career can mean to race around).
The initial letter of 'tutors' is 't'.
't'+'race'='TRACE'
(Other definitions for trace that I've seen before include "Vestige; manage to find" , "part of harness" , "Very small amount that can only just be detected" , "Discover - modicum" , "Vestige, hint" .)