King handily dismissing son in a deplorable way (8)
I believe the answer is:
ruefully
'king handily dismissing son' is the definition.
I can't judge whether this definition defines the answer.
'deplorable way' is the wordplay.
'deplorable' becomes 'rueful' (I've seen this in another clue).
'way' becomes 'ly' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'rueful'+'ly'='RUEFULLY'
'in a' acts as a link.
Can you help me to learn more?
(Other definitions for ruefully that I've seen before include "Loaded with regret" , "Contritely, remorsefully" , "Sorrowfully" , "In a regretful manner" , "In a wryly regretful way" .)