Crossword Genius

Puff a part of cigarette for Spooner to try (4,1,3)

Ross

I believe the answer is:

bust a gut

I'm a little stuck... Click here to teach me more about this clue!

'cigarette for spooner to try' is the definition.
I don't know anything about this answer so I can't tell whether it can be defined by this definition.

'puff a part' is the wordplay.
I cannot really understand how this works, but
'a' is present in the answer.
'part' could be 'bust' (busting is a kind of parting) and 'bust' is found in the answer.
The remaining letters 'gut' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'of' is the link.

Can you help me to learn more?

(Other definitions for bust a gut that I've seen before include "Make a strenuous effort" , "Really work extra hard" , "meet qualification for intestinal surgery?" , "Work extra hard to achieve something" , "Give it everything" .)

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