The most common and most likely answer to this crossword clue is the 7 letter word HEIRESS
I've seen this crossword clue in The Guardian
H
E
I
R
E
S
S
More clues leading to the result HEIRESS
- Woman who expects to succeed?
- Wildly theorises, but not to successor
- Someone having the potential to succeed
- Old Nazi full of rage? One has succeeded
- Passion-filled Nazi bigwig, one expected to succeed
- Inheritance outwardly hers? Could be, having succeeded
- Woman with eyes on family jewels?
- Woman succeeding?
- Dowager Dame Myra or Deputy Führer Rudolf suppressing rage
- Woman expecting money say in rise, she flips!
Buddy explains!

The straight part
We know that "successor" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case successor = heiress.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does HEIRESS mean?
HEIRESS noun- A woman who has a right of inheritance or who stands to inherit.
- A woman who has received an inheritance.