Get the better of graduate among new tutors (8)
I believe the answer is:
outsmart
'get the better of' is the definition.
(thesaurus)
'graduate among new tutors' is the wordplay.
'graduate' becomes 'ma' (abbreviation for Master of Arts).
'among' indicates putting letters inside.
'new' indicates anagramming the letters.
'tutors' is an anagram of 'outsrt'.
'ma' going into 'outsrt' is 'OUTSMART'.
(Other definitions for outsmart that I've seen before include "Outmanoeuvre cleverly" , "Cunningly get the better of" , "Fox; deceive" , "Defeat by more skilful manoeuvring" , "Win by clever thinking" .)