The Corellian Knights is a group of Jedi related to the Corellian Jedi who chose to serve The Organization secretly and become it's valued protectors and largest group of surviving Jedi after Order 66, are connected to not only The Organization, but also has deep connections to the Queen's Guardsmen and House of Royal Intelligence since The Organization and Red Rock Kingdom first met in 27,395 BBY.
Jim Palso, the famed time traveler from the New Republic Era, claimed that two Corellian Knights---dressed in white robes with gold edges and green lightsabers----offered him a position with them towards the end of his time with the Jedi Outcasts. If Jim Palso's story is true, then this would imply that both the Corellian Knights and The Organization have time traveling ability.
The precise nature of Corellian Knights in relation to The Organization is unclear, other then they appear to be the agency's protectors from the unknown or unseen and have the ability to time travel.
Jim Palso has been the only person ever recorded to see a Corellian Knight in such clothing attire and addressing themselves as Corellian Knights.