Rudely brief worker's method of rapid writing (9)
I believe the answer is:
shorthand
'rapid writing' is the definition.
(I've seen this before)
'rudely brief worker's method' is the wordplay.
I cannot really see how this works, but
'brief' could be 'short' (synonyms) and 'short' is located in the answer.
'worker' could be 'hand' (hand is a kind of worker) and 'hand' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
'of' acts as a link.
Can you help me to learn more?
(Other definitions for shorthand that I've seen before include "writing style" , "Method of abbreviated writing" , "Aid to taking dictation" , "Pitman's invention" , "Rapid writing language" .)