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Clerk, saving time, getting reward for a bit of a fag (6,3)

Ross

I believe the answer is:

filter tip

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'a fag' is the definition.
(I have seen 'A fag' mean 'filter tip' so perhaps 'fag' could also mean 'filter tip')

'clerk saving time getting reward for a bit' is the wordplay.
I cannot really see how this works, but
'time' could be 't' (abbreviation) and 't' is found in the answer.
'clerk' could be 'file' (file clerk is a kind of clerk) and 'file' is located in the remaining letters.
'reward' could be 'tip' (I have seen 'tiny reward' mean 'tip' so perhaps 'reward' could also mean 'tip') and 'tip' is found within the answer.
A single letter 'r' remains which might be clued in a way I don't understand.
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 filter tip that I've seen before include "Cigarette with an attachment for removing some of the harmful substances" , "Tobacco purifier" , "A fag" , "Cigarette feature" .)

I've seen this clue in The Times.
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