No early bird? (5-3)

I believe the answer is:

night-owl

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

'no early bird?' is the definition.
'night owl' can be an answer for 'bird?' (I've seen this before). I am unsure of the 'no early' bit.

'early bird?' is the wordplay.
'early' becomes 'night' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'bird?' becomes 'owl' (owl is a kind of bird).
'night'+'owl'='NIGHT-OWL'

Can you help me to learn more?

I've seen this clue in The Sun.

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