The Ancient Greek word for the type of acceptance I've been thinking about is most closely related to "acquiescence." [I'll have to explain why I think that word is best.] But that word is from Latin, not Greek, so I started looking at the Greek words for "quiet" and "to become quiet."
I find: ἡσυχία, rest of quiet personified; to be at peace or rest
In the Loeb Classics, it shows up in a number of places, but most interestingly in Pindar's 8th Pythian Ode where it is offered as a proper name: Ἡσυχία. The translator flags it for footnoting: "Hesychia, peace within the polis, is the daughter of Justice."
“And you notice, I think, when people get into many other similar situations in which, when they’re in pain, they praise not the feeling of joy but not being in pain and the relief from that sort of thing as the most pleasant sensation.”
“Yes, this is perhaps what then becomes pleasant and desirable: the relief,” he said.
Robert A. Bauslaugh links the term to "neutrality," as in political inaction due to policy.
Will Daddario is a historiographer, philosopher, and teacher. He currently lives in Asheville, North Carolina.