Graduate isn't coming back having got stick (5)
I believe the answer is:
baton
'stick' is the definition.
(term for a stick or staff)
'graduate isn't coming back' is the wordplay.
'graduate' becomes 'BA' (someone with a Bachelor of Arts degree).
'isn't' becomes 'not' (I can't justify this - if you can you should believe this answer much more).
'coming back' shows that the letters should be reversed in order.
'not' in reverse letter order is 'ton'.
'ba'+'ton'='BATON'
'having got' is the link.
Can you help me to learn more?
(Other definitions for baton that I've seen before include "Club, stick" , "Police (or conductor's) stick" , "Light wand" , "Relay race stick" , "It's passed in a relay race" .)