On 23rd March 2020 the Bishop of Southwark, Rt Revd Christopher Chessun, received a written answer to a question on visas for ministers of religion:

Baroness Williams of Trafford: Under the current Immigration Rules, there are a range of routes for specialist occupations, including Ministers of Religion and temporary religious workers.
There are no current plans to change these routes, though from January 2021, these routes will be opened to EEA citizens.