Eccentric, but not even a dance! (7)
I believe the answer is:
oddball
'eccentric' is the definition.
(an oddball is an eccentric person)
'not even a dance' is the wordplay.
'not even' becomes 'odd' ('odd' is the opposite to 'even').
'a dance' becomes 'ball' (ball is a kind of dance).
'odd'+'ball'='ODDBALL'
'but' is the link.
(Other definitions for oddball that I've seen before include "Bold lad (anag)" , "Nonconformist - peculiar" , "Eccentric person (colloq.)" , "Strange, bizarre" , "Strange person (colloq.)" .)