King brooded over duty (4)
I believe the answer is:
task
'duty' is the definition.
(task is a kind of duty)
'king brooded over' is the wordplay.
'king' becomes 'K' (abbreviation for king in chess).
'brooded' becomes 'sat' (to brood eggs is to sit on them).
'over' shows that the letters should be reversed in order.
'k'+'sat'='ksat'
'ksat' in reverse letter order is 'TASK'.
(Other definitions for task that I've seen before include "Assignment" , "Arduous bit of work" , "Set piece of work" , "Sort of force" , "commission" .)