Rule, then abdicate, failing to produce son (5)
I believe the answer is:
reign
'rule' is the definition.
(reign is a kind of rule)
'abdicate failing to produce son' is the wordplay.
'abdicate' becomes 'resign' (I've seen this in another clue).
'failing to produce' suggests deleting specific letters.
'son' becomes 's' (genealogical abbreviation for son).
'resign' with 's' taken out is 'REIGN'.
'then' is the link.
(Other definitions for reign that I've seen before include "Predominance" , "Hegemony" , "Sovereign's rule" , "Sit on a throne" , "Occupy the throne" .)