"Musical Priest", in Gaelic "An Sagart Ceolmhar" is also known as "The New Bridge Of Eden", "The New Bridge Of Erin".
It seems likely the "Musical Priest" was derived from Scots composer William Marshall's strathspey "Belhelvie House" (which the Gows renamed "The North Bridge of Edinburgh").
It was printed in both O'Neill's Music of Ireland: 1850 Melodies (1903) and The Dance Music of Ireland: 1001 Gems (1907).
It has been recorded by Callanish, Celtic Spring, Malcolm Dalglish And Grey Larsen, Gaelic Storm, De Dannan, The Dubliners, The Chieftains and many others.
I learned this at our Monday night jam.