Performing Rights are legal rights that protect a performer's right to perform live music in public. They are also part of Copyright law and there will be an accompanying legal agreement often known as a 'Performing Rights Agreement' which sets out what payments are paid to whom when such performances are carried out, which may involve a split between a composer (original author) and the performer/a publicist.
Such Agreements are often managed by Performance Rights Organisations as they have direct and relevant experience in collecting royalties on behalf of song writers and publishers for instance when their work is then played/ performed in public. Such Agreements will also cover if recordings of their work is used. This can also include streaming services however royalty payments are generally low compared to what would be paid in a public performance setting.
The advice to any songwriter or producer would always be that you should join a Performance Rights company and they in turn can liaise between different countries and jurisdictions as appropriate. It is not recommended to join different companies as you may then receive royalty payments from each which is not legally permitted and would be classed as fraud.
It is possible to assign or license the benefit of your Performing Rights either in your lifetime or on death. This is the same as with other forms of intellectual property rights.
As a performer for instance you will also have the 'moral right' to be identified as a performer and the right to object to any negative treatment in relation to that performance/ work. For instance, another performer would not be able to alter your work in a way that you be derogatory and/ or affect the original performer's reputation.
It is possible to sell, assign and gift your right to receive royalties, the benefits as detailed in a Performing Rights Agreement in your lifetime and on death, but copyright law has some critical rules that dictate who will receive a performer/ writers renewal or termination rights. This is even where there is a contrary intention in the Will.
Again another reason why it is so important that where any such Agreement does exist this is provided to the Will writer so they can advise you on what can be gifted and to whom; and further in what circumstance. The law in this area is very complex and you will always need to obtain specialist legal advice as one of the factors that is relevant and dictates how any such rights can be dealt with is when the copyright/ right came into existence.