Fat solidified across middle of cup (4)
I believe the answer is:
suet
'fat' is the definition.
(suet is a kind of fat)
'solidified across middle of cup' is the wordplay.
'solidified' becomes 'set' (I've seen this before).
'across' means one lot of letters goes inside another.
'middle of' indicates the central letters.
The middle of 'cup' is 'u'.
'set' enclosing 'u' is 'SUET'.
(Other definitions for suet that I've seen before include "Edible animal fat" , "Hard edible fat" , "Fatty stuff used in cooking" , "Hard animal fat used in cooking" , "Thin pancake" .)