I thought it would be fun/interesting to look at some of the potential arrivals at the Wall in the early part of The Winds of Winter.

Potential Arrivals at the Wall

Note: Not all of these characters will reach the Wall and some will likely die en route or be involved in plotlines elsewhere.

Kettleblacks

As far back as AFFC, Cersei was scheming to send Osney to the wall to kill Jon:

"This," Qyburn said. "For years now, the Night's Watch has begged for men. Lord Stannis has answered their plea. Can King Tommen do less? His Grace should send the Wall a hundred men. To take the black, ostensibly, but in truth . . ."

". . . to remove Jon Snow from the command," Cersei finished, delighted. I knew I was right to want him on my council. "That is just what we shall do." She laughed. If this bastard boy is truly his father's son, he will not suspect a thing. Perhaps he will even thank me, before the blade slides between his ribs. "It will need to be done carefully, to be sure. Leave the rest to me, my lords." This was how an enemy should be dealt with: with a dagger, not a declaration. "We have done good work today, my lords. I thank you. Is there aught else?"

and:

Even Mace Tyrell would not dare defend his darling daughter if she was caught in the act with the likes of Osney Kettleblack, and neither Stannis Baratheon nor Jon Snow would have cause to wonder why Osney was being sent to the Wall. She would see to it that Ser Osmund was the one to discover his brother with the little queen; that way the loyalty of the other two Kettleblacks need not be impugned. -AFFC, Cersei IV

Due to Cersei's incompetence/the new power of the Faith, Osney is no longer being sent to the wall and will instead be executed for killing the High Septon (Tyrion's).

There is a chance his brothers could still end up there:

What will you do with them?"

"The Wall, if they admit their guilt. If they deny it, they can face Ser Robert. Such men should never have been raised so high." -ADWD, Epilogue

If interested: Hostages of Ice and Fire

Ser Desmond Grell & Ser Robin Ryger

Two of Riverrun's garrison chooses to take the black:

Two men did not choose to depart with the others. Ser Desmond Grell, Lord Hoster's old master-at-arms, preferred to take the black. So did Ser Robin Ryger, Riverrun's captain of guards. "This castle's been my home for forty years," said Grell. "You say I'm free to go, but where? I'm too old and too stout to make a hedge knight. But men are always welcome at the Wall."

"As you wish," said Jaime, though it was a bloody nuisance. He allowed them to keep their arms and armor, and assigned a dozen of Gregor Clegane's men to escort the two of them to Maidenpool. The command he gave to Rafford, the one they called the Sweetling. "See to it that the prisoners reach Maidenpool unspoiled," he told the man, "or what Ser Gregor did to the Goat will seem a jolly lark compared to what I'll do to you." -AFFC, Jaime VII

It should be noted that Raff shows up in Braavos (think so?) in TWOW, Mercy I and doesn't mention the going to the Wall, or at all for that matter.

Its also possible that they decided to "dishonor" themselves and joined up with the BWB, etc:

The Tully garrison departed the next morning, stripped of all their arms and armor. Each man was allowed three days' food and the clothing on his back, after he swore a solemn oath never to take up arms against Lord Emmon or House Lannister. "If you're fortunate, one man in ten may keep that vow," Lady Genna said.

"Good. I'd sooner face nine men than ten. The tenth might have been the one who would have killed me." -AFFC, Jaime VII

Tycho Nestoris/Jeyne Poole/Justin Massey

“Oh, and take the Stark girl with you. Deliver her to Lord Commander Snow on your way to Eastwatch.” Stannis tapped the parchment that lay before him. “A true king pays his debts.”

Pay it, aye, thought Theon. Pay it with false coin. Jon Snow would see through the impostesure at once. Lord Stark’s sullen bastard had known Jeyne Poole, and he had always been fond of his little half-sister Arya.

“The black brothers will accompany you as far as Castle Black,” the king went on. “The ironmen are to remain here, supposedly to fight for us. Another gift from Tycho Nestoris. Just as well, they would only slow you down. Ironmen were made for ships, not horses. Lady Arya should have a female companion as well. Take Alysane Mormont.” -TWOW, Theon I

Stannis

We know that Stannis at least survives the Battle of Ice and burns Shireen:

It wasn't easy for me. I didn't want to give away my books. It's not easy to talk about the end of my books. Every character has a different end. I told them who would be on the Iron Throne, and I told them some big twists like Hodor and 'hold the door,' and Stannis's decision to burn his daughter. We didn't get to everybody by any means. Especially the minor characters, who may have very different endings." -SSM, Screenrant Article: 10 October 2020

If interested: The Cost: Stannis' Ultimate Sacrifice

Its possible that Stannis sends for Shireen as well instead of returning to the Wall.

There are plenty of other characters who could end up taking the black at some point, but this post was aimed primarily at those who are potentially headed there in the beginning of TWOW.

If you are interested in potential foreshadowing for characters joining the watch later in the series: The 1000th Commander of the Night's Watch

And if you want a look at the current status of what is going on at the wall: The Castle Black Plotline in The Winds of Winter

TLDR: A look at characters who could be headed to the Wall in the early parts of The Winds of Winter.