Crossword Genius

A close shave - the girl wasn't far off! (4,4)

Ross

I believe the answer is:

near miss

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

'a close shave' is the definition.
(I've seen this before)

'girl wasn't far off' is the wordplay.
I cannot quite see how this works, but
'girl' could be 'miss' (term of address for an unmarried woman) and 'miss' is found within the answer.
The remaining letters 'near' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'the' acts as a link.

Can you help me to learn more?

(Other definitions for near miss that I've seen before include "Attempt that just fails to be successful" , "Narrowly-averted accident" , "Close shave" , "Narrowly-avoided accident" , "Close call" .)

I've seen this clue in The Irish News.
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