A rum graduate, eccentric one (7)
I believe the answer is:
bacardi
'a rum' is the definition.
(I've seen this before)
'graduate eccentric one' is the wordplay.
'graduate' becomes 'ba'.
'eccentric' becomes 'card' (I've seen this before).
'one' becomes 'i' (Roman numeral).
'ba'+'card'+'i'='BACARDI'
(Other definitions for bacardi that I've seen before include "Drink" , "white spirit" , "White rum, first produced in Cuba" .)