Roman Catholic priests take a vow of Celebacy, to bind them more fully to the One, Holy, Catholic, Apostolic Church ... there are groups that call themselves “Catholic” ....
Not the married one. However, if his wife dies, he would not be permitted to remarry.
The Anglican priests that convert to Catholicism are grand-fathered in after taking the Catholic theology course. Nothing unusual here, given the status of the situation.
I believe our diocese has two such priests, both married.