Rt Rev Stephen Conway is sitting in the House of Lords in the week the Conservative Party will decide to appoint Jeremy Hunt or Boris Johnson as leader.
Bishop Stephen told Premier he acknowledged there was a lot of concern over the appointment but was praying that the UK would flourish under the new leadership.
"Everyone is rushing to tell us that whoever comes in has made impossible promises to the country and we're going to face a no deal Brexit with all the consequences that might follow," he said.
"I hope that the whoever is chosen as prime minister will seek immediately to assure the country that his priority is good governance, that he puts the interest of the nation first above party or any other consideration, and that he will not only model good practice for us, but in all of his endeavours be one who will speak the truth to us at all times and attend to our economy and our civil life so that we as a nation will flourish under his government."
With Boris Johnson is a clear favourite to succeed Theresa May, a government minister resigned on Monday.
Sir Alan Duncan left the foreign office warning that Brexit had cast a "dark cloud" over the country.
In June he described Mr Johnson as a "circus act".
His resignation comes after Chancellor Philip Hammond and Justice Secretary David Gauke both said they'd step down if Johnson becomes Prime Minister.
A result in the Tory leadership contest is expected between 11.30 and 12.30 on Tuesday.