British government abroad runs a judiciary initially (3)
I believe the answer is:
raj
'british government abroad' is the definition.
(the British Raj in India)
'runs a judiciary initially' is the wordplay.
'runs' becomes 'r' (cricket abbreviation).
'initially' suggests taking the first letters.
The first letter of 'judiciary' is 'j'.
'r'+'a'+'j'='RAJ'
(Other definitions for raj that I've seen before include "Sovereignty" , "British rule (in 19dn)" , "Indian rule in India" , "The period of British rule in India" , "Jar (anag.)" .)