Hi Zukki
There are a couple of possible scenarios here:
1. Room/Space/Chair Renter
Being a self-employed therapist renting an area within a Salon means that they are running their own stand-alone business, separate to the Salon's. They just happen to be physically located in the salon while they go about their trade.
The contractual relationship is therefore between the self-employed therapist and the Client that they provide the service to.
They should keep a record of each sale and take the cash/card each time themselves (the amount going into their business bank account).
They would then pay you a rental fee.
As a Salon, you would agree the terms of this relationship in a contract and it might be that as part of the rental fee they pay you, you take the cash for them at your till and pay the amount you owe them later (net of the rental fee they owe you).
So, the only invoicing needing to be done is one from you to the self employed therapist, for the rental fee each time it becomes due.
2. A contractor
This is different, in that their contractual relationship is with you as the Salon, rather than with the Client; and you might pay them an hourly rate.
As you rightly say, the onus is on you to ensure that HMRC do not consider them to be your employee rather than self-employed; and as the HMRC link from AcidPerm shows, this is a tricky area. If HMRC deem them to be an employee, they can come after you for PAYE tax and National Insurance (as well as a host of other responsibilities you would have as an employee, like holiday pay!)
My advice is to get a legal contract in place from a solicitor who deals in this area. Or, I know that as part of The NFH membership, you can help yourself to free contracts for chair renting that are already approved by them. And if you do, stick rigidly to the terms of the contract and you should be ok from an HMRC point of view.
Hope that helps but feel free to ask?