Harry died chasing barbarian around capital of Oman (5)
I believe the answer is:
hound
'harry' is the definition.
(both can mean to harass)
'died chasing barbarian around capital of oman' is the wordplay.
'died' becomes 'd' (abbreviation next to the year of someone's death).
'chasing' is a charade indicator (letters next to each other) (some letters chase after others).
'barbarian' becomes 'hun' (as in Atilla the Hun).
'around' indicates putting letters inside.
'capital of' says to take the initial letters.
The first letter of 'oman' is 'o'.
'hun' going around 'o' is 'houn'.
'd' put after 'houn' is 'HOUND'.
(Other definitions for hound that I've seen before include "badger" , "Hunting dog; harass" , "Pursue relentlessly" , "Breed of dog used for hunting" , "despicable creature" .)