Responsibility of old student group (4)
I believe the answer is:
onus
'responsibility' is the definition.
(thesaurus)
'old student group' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'student group' becomes 'nus' (National Union of Students).
'o'+'nus'='ONUS'
'of' is the link.
(Other definitions for onus that I've seen before include "'Burden, load (4)'" , "Weight of responsibility" , "Encumbrance" , "Responsibilty" , "Obligation - charge" .)