Wildly theorises, but not to successor (7)
I believe the answer is:
heiress
'successor' is the definition.
(thesaurus)
'wildly theorises but not to' is the wordplay.
'wildly' indicates anagramming the letters.
'but not' is a deletion indicator.
'theorises' with 'to' removed is 'herises'.
'herises' with letters rearranged gives 'HEIRESS'.
(Other definitions for heiress that I've seen before include "Female who will inherit riches" , "Portia, say" , "One who will inherit wealth" , "Woman likely to succeed?" , "Woman destined to succeed!" .)