After gym, sip fizzy soft drink (5)

I believe the answer is:

pepsi

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'soft drink' is the definition.
(Pepsi is an example)

'after gym sip' is the wordplay.
'after' means one lot of letters go next to another.
'gym' becomes 'pe'.
'sip' becomes 'psi' (I am not sure about this - if you are sure you should believe this answer much more).
'pe' put next to 'psi' is 'PEPSI'.

'fizzy' acts as a link.
This may not be right. It may belong to another bit of the clue.

Can you help me to learn more?

(Another definition for pepsi that I've seen is " drink".)

I've seen this clue in The Times.

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