Without a licence you would need to deal directly with the overseas composers, songwriters, music publishers, or other third parties who control the rights in the overseas song/s you wish to use.
An APRA AMCOS licence covers the majority of copyright music globally. APRA AMCOS has reciprocal agreements with collecting societies worldwide.
For example, PRS for Music administers Courtney Barnett’s rights in the UK, which means that royalties for performances in that territory are collected by PRS for Music and distributed to her accordingly via APRA AMCOS. Similarly, APRA AMCOS administers Ed Sheeran’s rights in Australia and pays his royalties accordingly through PRS for Music.