Traditionally, Quaker meetings recognized and nurtured individuals who had spiritual gifts as ministers, elders, or overseers. These roles could be filled by men or women, and their service extended over the entire congregation.
A person who offered vocal ministry during worship might be designated as a minister, if the messages were considered theologically sound. Because a minute would be drafted and approved in the meeting’s records, the individual would be known as a recorded minister.
Elders were those who held the ministers and ministry in prayer through the service. In other traditions, they might be called bishops, except that in Friends meetings, they function within the congregation, rather than over it. In the novel, Miz Lil and the Chronicles of Grace, Miz Lillian Leander upholds this role, even though her Lutheran denomination might not recognize its importance.
Overseers were individuals who were skilled in sensing the needs of others and in knowing how to respond. They were the ones who could transform the meeting for worship into a community of faith or a people of God.
After the painful divisions within the Society of Friends in the 1800s, these distinctions typically fell by the wayside. For quietist Meetings, there was an increasing aversion to hierarchy, especially one where ministers or elders might be appointed for life; other Friends, especially those west of the Appalachian Mountains, moved progressively toward services led by a pastor – someone who was often expected to embody all three gifts.
Still, the work’s there to be done, by somebody. Some forms, I’ll argue, work better than others.
Jnana's Red Barn 
When you say Quietist, do you mean the same as some mean by Conservative/ Wilburite? In the UK, some speak more of having elders more visible and active, talking to Friends more, more active in chiding.
My use goes to the definition of those who seek or enjoy quiet.
I’ve been looking for an alternative to the Quaker-speak of “unprogrammed” meeting, in contrast to a “pastoral” or “programmed” meeting. (Yes, while those of you in the U.K. hew to the traditional “waiting worship,” much of the Quaker world today has worship led by a pastor, which is why I’m looking for a term in the first place.) Or, for that matter, a “silent” meeting, which really isn’t accurate, either. Even when there’s no speaking, there are still noises everywhere.
Complicating the matter is a Roman Catholic movement known as Quietists. Alas!
I’m open for (new) suggestions.
What about something around that we all pastor each other? A “mutually pastoring” meeting, perhaps.