Examiner with case of coursework entering lift (7)
I believe the answer is:
checker
'examiner' is the definition.
(checker is a kind of examiner)
'case of coursework entering lift' is the wordplay.
'case of' suggests removing the centre (outsides of).
'entering' means one lot of letters goes inside another.
'lift' becomes 'cheer' (lift can mean to cheer up).
'coursework' with its centre removed is 'ck'.
'ck' placed within 'cheer' is 'CHECKER'.
'with' is the link.
(Other definitions for checker that I've seen before include "Scrutiniser" , "one dispatched to vet?" , "Verifier" , "One making sure" , "a man in America" .)