Not having a good time he was easily beaten (4,6)

I believe the answer is:

poor second

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

'not having a good' is the definition.
I don't know anything about this answer so I can't judge whether this works.

'time he was easily beaten' is the wordplay.
I cannot really see how this works, but
'time' could be 'second' (I've seen this before) and 'second' is present in the answer.
The remaining letters 'poor' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in The Globe and Mail.

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