Clever chap having nagging woman stop (8)

I believe the answer is:

shrewdie

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

'clever chap' is the definition.
The definition suggests a singular noun which matches the answer.

'nagging woman stop' is the wordplay.
'nagging woman' becomes 'shrew' (I've seen this in another clue).
'stop' becomes 'die' (I've seen this in other clues).
'shrew'+'die'='SHREWDIE'

'having' is the link.

Can you help me to learn more?

I've seen this clue in The Times.

Want a hint initially instead of a full solution? Install my app