Yes, they do get paid.
Also known by the name of Hazzan, the role of Cantor is one of the two ministerial positions in a Jewish Synagogue, the other being a Rabbi. The main responsibility of a Cantor is to present liturgical music that helps in clarifying studies and prayers in a synagogue or temple. This music augments the experience of worshippers, as the Cantor leads them in prayer.
When the congregation selects a candidate for this prestigious position, historically a starting salary is decided through negotiation. Part-time positions especially for the High Holidays are very common.
The Cantorial profession is in decline as memberships in communities have dwindled and synagogue budgets are greatly challenged. Still, there are Cantors who serve as sole Spiritual Leaders of their communites.
JSLI prepares students to "daven" (pray) with traditional "Nusach" (religious musical modes).