Those jobs are bishop or church organist.
Being a bishop means spending your career in dwindling relevance and attending meetings every evening of the week with people who can't wait for you to leave the room so that they can complain about you. [Hey, wait a minute. That sounds like a rector, too. Hmmm.]
Being a church organist means the very deliberate work of planning music that matches liturgy, season, and the general mood and talents of the congregation and community. If the occasion is celebratory, the music should provide a lyrical stream on which the high emotions of the congregation may ride. If the occasion is dour or mortal, the music lifts up the resurrection inherent in our prayers and practice.
One year, the congregation may ask for more choir music at Christmas or Easter; and the next year complain that music was awful and they want more carols and hymns, which largely then go un-sung by the congregation, prompting a fresh round of criticism. Then, they'll ask for more choir music. All this plus terrible pay and having to work with eccentric clergy.
But, every once in a while, someone, say a reporter for The Guardian, will write a marvelous appreciation of the role of music and Evensong as it is known through our form of Christianity:
And then there is the music itself. The best theologians are musicians. And Christianity is always better sung than said. To the extent that all religion exists to make raids into what is unsayable, the musicians penetrate further than most. When Mendelssohn takes the words of Psalm 55 and transforms them into the almost unbearably moving Hear My Prayer, he is not offering up some theological argument that can be batted about, agreed with, disagreed with. It's not propositional. It's a cry from the depths of his being. Longing, joy, hope, hopelessness, the call for justice – all these get expressed by religious music in ways that religious words can only partially capture.