Likely candidates thus far:
Zemo
John Walker, aka US Agent
Yelena
Taskmaster
Abomination (confirmed in both Shang-Chi and She-Hulk)
Ghost (from Antman and the Wasp)

Since Barton is the target, I doubt he'll be on the team. Kate Bishop (the new Hawkeye) will be part of the Young Avengers, another team that is being set up and we've seen multiple likely members already:
Kate Bishop
Wanda's 2 kids Speed and Wiccan
The kid in FatWS, Eli Bradley
Cassie Lang
Kid Loki
America Chavez (coming in Doctor Strange 2)