Here's my thoughts on what the post-TG careers of certain characters might be (assuming that they survive and that Avi's view of the future doesn't come true):

Nynaeve: helping rebuild Malkier

Elayne: spends most of the next 20-25 years ruling Andor and Cairhien, with a little dabbling in *greal study. Then, when her daughter is grown, married and has produced an heir or two, Elayne steps down as queen. She then can devote herself to study and production of *greals and on the side, becomes a permanent Arbiter of Succession Rights for the inevitable future occasions when there's doubt about the proper successor to the throne.

Egwene: continues being Amyrlin for the next couple or three centuries, casting particular terror into the poor novices/Accepted/exchange students who have to study dreamwalking under her supervision.

Moiraine/Thom: become roving spies for the Amyrlin Seat, keeping a close eye on the intrigues of the various royal courts of Randland.

Morgase/Tallanvor: Morgase becomes Elayne's Regent in Cairhein, running things on a day-to-day basis when Elayne can't be there.

Siuan/Gareth: Siuan becomes Elayne's Aes Sedai advisor and also serves as the Tower's official liaison to the Kin. One of her duties as liaison would be to help the Kin search out new candidates for the Tower.