King’s daughter succeeded after his sons? (8)
I believe the answer is:
princess
'king's daughter' is the definition.
(a daughter of a monarch is a princess)
'succeeded after his sons?' is the wordplay.
'succeeded' becomes 's' (genealogical abbreviation).
'after' means one lot of letters go next to another.
'his' becomes 'prince' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
's' after 'prince' is 'princes'.
'princes'+'s'='PRINCESS'
(Other definitions for princess that I've seen before include "Royal lady" , "Female aristocrat" , "Part of royalty" , "Royal girl" , "Royal daughter" .)