It's odd the band should start with dance music (5)
I believe the answer is:
rumba
'dance music' is the definition.
(I know that rumba is a type of dance music)
'it's odd the band should start' is the wordplay.
I cannot really see how this works, but
'odd' could be 'rum' (rum can mean strange or dubious) and 'rum' is found in the answer.
The remaining letters 'ba' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'with' is the link.
Can you help me to learn more?
(Other definitions for rumba that I've seen before include "Ballroom dance of Cuban origin" , "One from Cuba" , "Strictly round" , "one's on the floor for it" , "number of steps" .)