Performer rights
Performers e.g. dancers and actors have rights over their work. This includes giving permission for recording of their works and controlling what can be done with their performances. You will need to get permission or check licenses for this.
Music for teaching
For teaching purposes only sound recording are permitted. When the audience are staff and students only.
Should this not be the case you will need a license
Music licensing organisations
PRS for music (licensing for music composers)
PPL (licensing for peformers and record companies)
From June extracts of off air recordings can be copied for using in teaching or instruction.