Provide evidence for a tutor’s first examination (6)
I believe the answer is:
attest
'provide evidence for' is the definition.
(I've seen this before)
'a tutor's first examination' is the wordplay.
'first' says to take the initial letters.
'examination' becomes 'test' ('test' can be a synonym of 'examination').
The first letter of 'tutors' is 't'.
'a'+'t'+'test'='ATTEST'
(Other definitions for attest that I've seen before include "Provide firm evidence" , "Sign on" , "Offer evidence" , "Declare (that something is the case)" , "Give evidence in a court of law" .)