None! The Stream is fully licensed for business use globally which means no risk of fines and the artists are fully compensated for their work.
The Stream has been designed for use in spas so once you sign up for a free trial/purchase the subscription you have instant access. Whether you're in the US or UK or elsewhere around the world you do not need a separate public performance license to play music from The Stream in your spa setting which could save you thousands in annual licensing fees.
Please note: these licences do not cover you performing any of the music, content or related content outside of the The Stream service. Full T&Cs are here.