DAERA and Loughs Agency each sell angling licences for their specific areas (see map) so the type of licence you need, will depend on the area you choose to fish in.
The fisheries managed by DAERA are known as the Public Angling Estate (PAE). These fisheries are open to the public and are listed at the following link where you'll also find private fisheries that are not managed by DAERA.
Private fisheries are known as 'fisheries outside the Public Angling Estate' - they're also open to the public and include Loughs Agency managed fisheries: