Live race in Irish island kingdom (6)

I believe the answer is:

brunei

I'm a little stuck... Click here to teach me more about this clue!

'island kingdom' is the definition.
The answer and definition can be both locations as well as being singular nouns.
Maybe they are linked in a way I don't understand?

'live race in irish' is the wordplay.
'live' becomes 'be' (synonyms).
'race' becomes 'run' (synonyms).
'in' means one lot of letters goes inside another.
'irish' becomes 'i' (this could be a standard abbreviation I've not previously seen).
'be' going around 'run' is 'brune'.
'brune'+'i'='BRUNEI'

Can you help me to learn more?

(Other definitions for brunei that I've seen before include "It's sultan is immensely rich" , "North Borneo sultanate" , "Its sultan is famously very wealthy" , "Commonwealth country" , "Southeast Asian sultanate" .)

I've seen this clue in the Sydney Morning Herald.

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