As Joe Schoen and Brian Daboll begin their respective tenures as the general manager and head coach of the Giants, they have made clear a desire for stability at a number of positions in the organization. As Ian Rapoport of NFL Network reports (via Twitter), the team plans on retaining defensive coordinator Patrick Graham if he doesn’t get a HC gig elsewhere. As well, his colleague Mike Garafolo tweets that assistant GM Kevin Abrams and director of football operations Ed Triggs will be staying with the team. 
Graham, as Rapoport notes, recently interviewed with the Vikings for their HC vacancy. That came after he met with the Giants for the same position; while he obviously didn’t get the top job in New York, the team has let it be known they respect his work as DC.
In his inaugural press conference on Monday, Daboll – who worked alongside Graham for three seasons in New England – said, “I have had a good relationship with Pat for some time in this league. He’s very diligent. He’s smart. I think the players respect him. I have a good working relationship with him. Selfishly, I would love him to be here“. As the Athletic’s Dan Duggan tweets, defensive backs coach Jerome Henderson is expected to be retained as well.
As for Abrams, it appears he will be staying in New York, but quite possibly with a new title. As Duggan tweets, he has “offered to give up” the assistant GM label if it helps Shoen bring in a more familiar right-hand-man. Having been with the Giants since 1999, Abrams was a candidate for the GM opening, but the team stuck to its stated intention of hiring externally.
Triggs, meanwhile, has held his current role since June 2020 and like Abrams, has a plethora of front office experience with the Giants. Clearly, Shoen and ownership want to keep key elements of the existing executive structure in place, as opposed to clearing house as other teams have done in the past.