Eccentric degree students are after rum (7)
I believe the answer is:
oddball
'rum' is the definition.
(rum can mean strange)
'eccentric degree students are after' is the wordplay.
'eccentric' becomes 'odd' (I've seen this before**).
'degree' becomes 'ba' (Bachelor of Arts).
'students' becomes 'll'.
'are after' says to put letters next to each other.
'odd'+'ba'+'ll'='ODDBALL'
(Other definitions for oddball that I've seen before include "Strange, bizarre" , "Crank" , "Nonconformist - peculiar" , "Bold lad (anag)" , "Strange person (colloq.)" .)