Vital European killers finally dispatched one gangster (9)
I believe the answer is:
essential
'vital' is the definition.
('essential' can be similar in meaning to 'vital')
'european killers finally dispatched one gangster' is the wordplay.
'european' becomes 'e' (abbreviation e.g. EU).
'finally' indicates one should take the final letters.
'dispatched' becomes 'sent' (I've seen this before).
'one' becomes 'i' (Roman numeral).
'gangster' becomes 'al' (Al Capone).
The final letter of 'killers' is 's'.
'e'+'s'+'sent'+'i'+'al'='ESSENTIAL'
(Other definitions for essential that I've seen before include "Type of oil" , "'Absolutely necessary, required (9)'" , "Key" , "Crucial" , "So is certain oil-production" .)