Dance piece with no intro being put in again (2-8)

'dance piece' is the definition.
The definition suggests a singular noun which matches the answer.

'no intro being put in again' is the wordplay.
I cannot quite understand how this works, but
'no' could be 'o' (resembles 0 - 'no' can mean 'zero') and 'o' is located in the answer.
'in' is within the answer.
'again' could be 're' (prefix meaning 'again') and 're' is found within the answer.
The remaining letters 'elect' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

'with' acts as a link.

Can you help me to learn more?