It is a good idea to have a written agreement with session musicians that covers issues such as copyright in the music and recording, moral rights, performers’ rights, and whether or not they are entitled to any additional payment for their contribution (either as an additional up-front payment or as a downstream royalty).
Note that, for recordings made after 1 January 2005, unless the recording is commissioned or the session musicians otherwise agree, they will also have a claim to a share in the copyright of the sound recording.
Performers also have some very limited rights in relation to recordings made before 1 January 2005. Even for future recordings, performers’ rights are likely to be very limited in practice as a result of a number of the provisions. In particular, if a recording of a performance is made for a fee (for example, a record company contracts with a production studio to produce a master recording), the performer will have no rights.
If a session musician is improvising for a recording, or their improvisation is recorded at a live gig, they could be a co-writer of that particular version of the material. In a case in the UK, a session violinist was able to establish he owned copyright in a riff he had created in a recording session and on that basis was able to claim a proportion of the royalties in that piece.