Eccentric American tenor inside? Sauce! (7)
I believe the answer is:
custard
'sauce' is the definition.
(I've seen this before)
'eccentric american tenor inside?' is the wordplay.
'eccentric' becomes 'card' (I've seen this before**).
'american' becomes 'us'.
'tenor' becomes 't'.
'inside?' means one lot of letters goes inside another.
'us'+'t'='ust'
'card' placed around 'ust' is 'CUSTARD'.
(Other definitions for custard that I've seen before include "Sweet sauce made with milk and eggs" , "Pudding accompaniment" , "Pudding sauce" , "Type of apple" , "Egg/milk bake" .)