If I cut the core out, there will be a hole (7)
I believe the answer is:
orifice
'a hole' is the definition.
(thesaurus)
'if i cut the core out' is the wordplay.
'cut' indicates an anagram.
'out' means one lot of letters goes inside another.
'core' anagrammed gives 'orce'.
'if'+'i'='ifi'
'ifi' inserted within 'orce' is 'ORIFICE'.
'there will be' is the link.
(Other definitions for orifice that I've seen before include "Space" , "Hole, opening" , "provided by gold and diamonds" , "Bodily hole" , "8 [OPENING]" .)