Local police penning poem about pretty vapid figure (6,4)
I believe the answer is:
barbie doll
'pretty vapid figure' is the definition.
I know nothing about this answer so I can't judge whether this works.
'local police penning poem' is the wordplay.
'local' becomes 'bar' (local can mean someone's local pub).
'police' becomes 'bill' (informal term for UK police).
'penning' means one lot of letters goes inside another.
'poem' becomes 'edo' (I can't explain this - if you can you should give a lot more credence to this answer).
'bill' going around 'edo' is 'biedoll'.
'bar'+'biedoll'='BARBIE DOLL'
'about' is the link.
Can you help me to learn more?
(Other definitions for barbie doll that I've seen before include "Artificial and attractive woman" , "Glamorous toy" .)