The majority of venues in the UK & Ireland are covered through entertainments licences that are purchased for the performance of live and non-live music. This is regulated by a body called PRS (Performing rights society). This means that music you purchase / download is covered by the venues licence and therefore there is no need to obtain a separate licence or permission to play these tracks.
I’m not sure what the rules are for other countries but that’s how it works here..
Cheers,
Chris