In the manner of conservative king's expression of regret (5)
I believe the answer is:
alack
'expression of regret' is the definition.
(archaic word expressing sorrow or regret)
'in the manner of conservative king's' is the wordplay.
'in the manner of' becomes 'a la' ('a la' means 'in the manner of', as in 'a la mode').
'conservative' becomes 'C' (UK political abbreviation).
'king' becomes 'K' (abbreviation for king in chess).
'ala'+'c'+'k'='ALACK'
(Other definitions for alack that I've seen before include "expression of regret" , "Old expression of dismay" , "I mourn" , "unfortunately" , "I'm sorry to say" .)