Asian banker’s application not given to judge (5)
I believe the answer is:
indus
'asian banker's' is the definition.
(a river, ie something with 'banks')
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for indus that I've seen before include "Largest river of Pakistan" , "Asian runner" , "River giving its name to an early civilisation" , "River rising in Tibet" , "9 of Pakistan" .)