Am older, bursting to succeed to this? (7)
I believe the answer is:
Here is my best explanation:
'succeed to this?' is the definition.
'am older bursting' is the subsidiary indication.
'bursting' indicates an anagram.
'amolder' with letters rearranged gives 'earldom'.
'to' is the link.
(Other definitions for earldom that I've seen before include "Units", "Norfolk or Wessex, for example", "A noble's lands or title", "Noble rank", "Noble's lands or rank", "Lands of a nobleman", "Nobleman's estate", "Peer's rank", "Title or estates of a nobleman" and "Noble's status".)