The early marketing for Top Gun: Maverick hasn't revealed much about Maverick's relationship with Bradley in the present day, although he is very close to Goose's whole family when Goose is still alive. The official synopsis for the new movie, captioning the first trailer, seems to imply that Maverick and Bradley aren't close these days:
"When he finds himself training a detachment of Top Gun graduates for a specialised mission the likes of which no living pilot has ever seen, Maverick encounters Lt. Bradley Bradshaw (Miles Teller), call sign: "Rooster," the son of Maverick's late friend and Radar Intercept Officer Lt. Nick Bradshaw, aka "Goose." Facing an uncertain future and confronting the ghosts of his past, Maverick is drawn into a confrontation with his own deepest fears, culminating in a mission that demands the ultimate sacrifice from those who will be chosen to fly it."