The main characters:
Allura would be the black paladin, and instead of being a teenager would be an adult around the same age as Shiro, the way the Voltron fandom initially thought she was. Which would make her and Shiro around 23 years old.
Lance would stay the blue paladin
Keith would stay the red paladin
Keith and Lance would be childhood rivals turned friends who would become a couple over the course of the series.
Hunk would be the yellow paladin
Pidge would be the green paladin and would be a child prodigy being the youngest of the paladins at the age of 16, while Lance, Hunk and Keith would be 18 years old.
Shiro would be Keith's biological brother, and would get to marry Adam who wouldn't die in this version. His role in this reboot would be similar to the role he played as the captain of the Atlas during the last two season of VLD and the role Allura had during the first two seasons of VLD.
Outside of the paladins and Shiro, here are the other major characters I would want to play a role in my idea for a Voltron reboot:
The Galra:
Former emperor Zarkon
Empress Hagar
Admiral Sendak
Resistance Leader Kolivan
Prince Lotor
The Alteans:
King Alfor
Allura's cousin Romelle
Royal Adviser Merla
Galaxy Garrison/Earth
Admiral Sanda
Commander Iverson
Commander Adam