Head of old Oxford debating society abandoning university (5)
I believe the answer is:
onion
'head' is the definition.
(I've seen this before)
'old oxford debating society abandoning university' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'oxford debating society' becomes 'union' (Oxford Union).
'abandoning' suggests deleting specific letters.
'university' becomes 'u'.
'union' with 'u' removed is 'nion'.
'o'+'nion'='ONION'
'of' is the link.
(Other definitions for onion that I've seen before include "Hot dog topping" , "Plant with edible bulb" , "Strong tasting vegetable" , "Shape of Russian dome" , "Type of allium" .)