Vacuous personnel piercing nipple? That just won't happen (5,6)

'just won't happen' is the definition.
I know nothing about this answer so I can't judge whether it can be defined by this definition.

'vacuous personnel piercing nipple?' is the wordplay.
I cannot quite see how this works, but
'vacuous' could be 'empty' (synonyms) and 'empty' is present in the answer.
'personnel' could be 'hr' (Human Resources) and 'hr' is located in the answer.
'nipple?' could be 'teat' (synonyms) and 'teat' is located in the leftover letters.
No letters remain.
This explanation may well be incorrect...

'that' is the link.

Can you help me to learn more?