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Third party insurance for a girl out socially (8)

Ross

I believe the answer is:

chaperon

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

'third party' is the definition.
The definition and answer can be both people as well as being singular nouns.
Perhaps there's a link between them I don't understand?

'insurance for a girl out socially' is the wordplay.
I cannot quite see how this works, but
'a' could be 'per' (eg 'one a day' means 'one per day') and 'per' is found in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for chaperon that I've seen before include "Accompany and look after" , "Escort" , "One accompanies to supervise" , "Guardian" , "Girl minder from Cape Horn" .)

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