On 15 June 1986, Dávid Tencer received the sacrament of priestly ordination for the Diocese of Banská Bystrica.

In 1990, Tencer entered into the Order of the Capuchins, and on 28 August 1994 he made his perpetual profession.

In 2007, he was made parish priest of the St. Thorlak Church in Reyðarfjörður, He also served on the Presbyteral Council and on the Diocese's Collegium Consultorum.

His co-consecrators were the apostolic nuncio in Iceland, archbishop Henryk Józef Nowacki, and the bishop of Žilina, Tomáš Galis.

On 17 June 2017 a new Catholic Church was consecrated in Reyðarfjördur in a ceremony led by Tencer.