I did it at Oxford writing to heir apparent (9)
I believe the answer is:
successor
'heir apparent' is the definition.
(thesaurus)
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for successor that I've seen before include "New leader" , "One taking over from another" , "one will take your place" , "I follow" , "Heir" .)