That would depend upon what type of priest he happens to be. If he is a secular priest he would probably live in a rectory. A rectory is a house, usually near to the Church, set aside for the clergy of that Church to live. If he is a priest of a religious order he might live in a convent or a monastery.
They can be called priories, rectories, presbyteries or religious houses as well as monasteries or convents.
Typically, the living quarters of the priest is referred to as a rectory.
A Rectory is the residence for a parish priest.
The Presbytery
Rectory
It usually depends on the priest's title; a rector lives in a rectory, a vicar lives in a vicarage and a parson lives in a parsonage. A Catholic priest usually lives in a parochial house. "Important" Bishops often live in palaces. The Scottish Presbyterian Church residence is called a 'Manse' - & if the property is later sold for non-church use, the new owner is prohibited from naming the property as 'The Manse'
A living place where an organism lives is called a habitat.
A person who lives in a particular place is called a resident.
In a general sense, a Catholic priest usually lives in a rectory. It is a house provided by the church for the comfort of the priest. Usually, it is a house that would be common in a given area.
It is where the priest lives
habitat
manse
the woods
An eagle nest is called an aerie.
A habitat.
habitat
It lives in a mgical place called Sloth Valley.