Churches are allowed to play CDS and music recordings during their Sunday services without requiring a licence from CCLI.
However, if a church is using CDs or music recordings in the church office or at ministry that doesn’t occur during the main church services, then it is quite likely you will need a CCLI  licence.

There is also another organisation called PPCA who also owns rights within CDS and music recordings.
If you need a CCLI licence due to using CDS and music recordings outside of the Sunday service, then it is a good chance that you will also need a PPCA (Phonographic Performance Company of Australia) licence.