To play live (or as-live) on radio is simple, the station just pays the usual per-song fee they usually pay for other shows. This would then cover them for the usual listen again features and live streaming.

If they then wanted to release it on CD or make it downloadable then they would have negotiate as usual for music releases, which is considerably more expensive. There's a bit about the pain of clearing music inside the sleeve of on one of the Soulwax, as heard on Radio Soulwax CD.