Abdication, but not wanting son on the throne ... (8)
I believe the answer is:
reigning
'abdication but not wanting son' is the definition.
I can't tell whether this definition defines the answer.
'on the throne' is the wordplay.
I cannot really understand how this works, but
'on' could be 're' ('on' can be mean 'with reference to') and 're' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Another definition for reigning that I've seen is " Ruling over like a sovereign".)