Insignificant banker's unacceptable service on the back of jet (9)
I believe the answer is:
streamlet
'insignificant banker's unacceptable' is the definition.
I can't tell whether this definition defines the answer.
'service on the back of jet' is the wordplay.
'service' becomes 'let' (type of tennis serve).
'on' is a charade indicator (letters next to each other).
'the back of jet' becomes 'stream' (I am not sure about this - if you are sure you should believe this answer much more).
'let' put after 'stream' is 'STREAMLET'.
Can you help me to learn more?
(Other definitions for streamlet that I've seen before include "hardly a river" , "Burn" , "small brook" , "running water" .)