Go down and see graduate getting certificate (7)
I believe the answer is:
diploma
'certificate' is the definition.
(academic certificate)
'go down and see graduate' is the wordplay.
'go down' becomes 'dip' (to dip is to go down or go under).
'and' is a charade indicator (letters next to each other).
'see' becomes 'lo' ('lo' is an archaic exclamation meaning 'look!').
'graduate' becomes 'MA' (abbreviation for Master of Arts).
'dip'+'lo'+'ma'='DIPLOMA'
'getting' is the link.
(Other definitions for diploma that I've seen before include "Academic certificate" , "Honorific document" , "What a student seeks" , "degree certificate" , "Document conferring a qualification" .)