Eccentric person eating only skimmed milk-based sauce (7)
I believe the answer is:
custard
'milk-based sauce' is the definition.
'eccentric person eating only skimmed' is the wordplay.
'eccentric person' becomes 'card' (card can informally mean an eccentric).
'eating' means one lot of letters goes inside another.
'only' becomes 'just' (synonyms).
'skimmed' means to remove the first letter (to skim something is to take the top off it).
'just' with its first letter removed is 'ust'.
'card' enclosing 'ust' is 'CUSTARD'.
(Other definitions for custard that I've seen before include "Pudding accompaniment" , "Yellow sauce" , "Dessert sauce" , "Pudding sauce" , "Sweet sauce made with milk and eggs" .)