The former vicar of the United Benefice of All Saints, Catherington, and St James, Clanfield, the Rev Chris Beardsley, has legally changed his identity and is officially a woman.
The Rev Beardsley left the benefice last year and was licensed as a part-time chaplain at Southlands Hospital, Shoreham.
The Bishop of Chichester, the Rt Rev John Hind, believes that the licence should be relinquished voluntarily but the Rev Beardsley has decided not to do so.
The law supports that decision: under current legislation the bishop may not revoke the licence.
The bishop has asked that everyone should respect "the huge personal anguish" which must have led to the Rev Beardsley's decision and refrain from intrusive enquiry and speculation.