Unit of energy used by eccentric or Celia (7)
I believe the answer is:
calorie
'unit of energy' is the definition.
(I've seen this before)
'eccentric or celia' is the wordplay.
'eccentric' is an anagram indicator.
'or'+'celia'='orcelia'
'orcelia' is an anagram of 'CALORIE'.
'used by' is the link.
(Other definitions for calorie that I've seen before include "Unit of heat (concerned with diet)" , "Food energy unit" , "generating a bit of heat" , "Oil race (anag)" , "Unit of heat energy" .)