US Olympic gymnasts who could qualify for the vault final: It goes without saying that Biles will qualify and win the vault final. Salim-Beasley predicts that Carey, competing as one of the two individuals for the US, will also make the vault final. She stated that though MyKayla Skinner, the other individual American athlete, is dominant on vault, she believes Carey has better execution, and if they compete similar vaults, Carey would out-perform Skinner due to her cleaner form. I agree to an extent; Carey, in my opinion, has better execution when it comes to height off of the vaulting table, but Skinner is still a great vaulter. For reference, they are capable of competing the same vaults in competition, so it'll be a close call.
Olympic artistic gymnastics vault final podium contenders: If all goes as planned, Biles will walk away with a gold on vault, and she doesn't even have to do her Yurchenko double pike, which is the highest-valued vault in women's artistic gymnastics right now, in order to win. As for the next two podium spots, Sacramone Quinn does think that Skinner has a shot. My vote is that I personally am leaning toward Carey as a medal contender due to her decorated history and consistency in recent years (though, to be fair, Skinner spent three years on the collegiate level, so it's tricky to compare).
Sacramone Quinn and judge Chan both think that individual Swiss gymnast Giulia Steingruber has a shot at a medal. She most recently won gold on this event at the 2021 European Championships (it was her fourth vault title at these championships). Steingruber is also the 2016 Olympic bronze medalist on vault.
Another contender for vault in Chan's eyes is Canada's Shallon Olsen, who received eighth in the vault final at the 2016 Olympics. Chan named Olsen's vault silver medal at the 2018 World Championships and gold medal at the 2018 Commonwealth Games as indications of her potential at the Olympics on this event.
One person I do not want to rule out completely is Uzbekistan's Oksana Chusovitina, who is known as a vault specialist and is heading to her record eighth Olympic Games. She was the Olympic vault silver medalist at the 2008 Beijing Games and consistently upgrades her difficulty through the years. She won't be a top contender, and it remains to be seen if she'll make it into the final, but if she does, I wouldn't put it past her to execute her hardest vaults to vie for third place (as The Balance Beam Situation points out, Chusovitina has a vault worthy of a 5.8 difficulty value, the same as the Amanar, which is a vault that Carey, Skinner, and Biles do).
The Olympic artistic gymnastics vault final is slated for Aug. 1.