Core or centre (7)
I believe the answer is:
nucleus
This clue is a double definition.
'core' is the first definition.
(synonyms)
'centre' is the second definition.
(nucleus is a kind of centre)
(Other definitions for nucleus that I've seen before include "Heart of the Matter" , "Central mass - kernel" , "Atom's core" , "Core, centre" , "hard core" .)