Currently, ACF v4 does not offer any back-end functions to render out a field.
Perhaps the easiest way is for your AJAX to return JSON data of all the new choices, and then you can append the choices via JS?
Welcome to the Advanced Custom Fields community forum.
Browse through ideas, snippets of code, questions and answers between fellow ACF users
ACF wouldn’t be so widely used in WordPress if it didn’t have some pretty amazing capabilities. In this article, we look at a few of the features we’ll discuss during “7 things you didn’t know you could do with ACF” at #WPEDecode later this month. https://t.co/5lnsTxp81jpic.twitter.com/Yf0ThPG1QG