There are two main musical rights organisations you may have to deal with for live performance in a venue. You can head to their websites for more info through the links provided below:

APRA AMCOS

APRA AMCOS deals with music creators (e.g. a lyricist or composer), and makes sure they are properly reimbursed for the use of their work.

OneMusic

OneMusic is a new organisation, designed to simplify the licensing process by combining the above organisations.