Brady swapped the New England Patriots for the Buccaneers in the NFC South via free agency after a glorious 20-year run and six Super Bowl rings in Foxborough.
The Patriots have won 11 consecutive division titles – and three Super Bowl championships during that period – thanks to superstar quarterback Brady.
But Gore feels the balance of power has shifted in the AFC East, where the Jets, Buffalo Bills and Miami Dolphins are looking to dethrone the Patriots.
"It's wide open," the 37-year-old said via a videoconference call with reporters on Thursday. "Brady's gone, and it's wide open.
"You've got young quarterbacks, Sam Darnold and Josh [Allen]. I don't know what Miami is doing or whatever. I think it's wide open."
Gore is preparing for his first year with the Jets after brief spells with the Bills and Dolphins.
The five-time Pro Bowler has reunited with head coach Adam Gase following the pair's time together in Miami, while the latter's relationship with star Le'Veon Bell has dominated headlines.
Bell struggled during his first season in New York and Gase is looking to lighten the workload for the three-time Pro Bowler.
On Bell, Gore said: "I told him I need a jersey to put on my wall just because I respect his game. I respect the way he prepares himself to get ready for the season.... He always respected me; I respected him.
"It will be fun. I've been around a bunch of talented running backs my whole career -- college, the NFL. I'm going to do whatever it takes to help him, to help the other guys and also help the team be successful."
"I'm cool," Gore added. "I'm happy to be playing this game at my age. I'm happy that this organisation is giving me an opportunity. I'm just coming in to work and help all the young guys, and show them young guys I still can play. Whenever I get my number called, I'll just try to go out and make a play for our team to be successful. I'm very excited."
Five-time Pro Bowler Gore turns 39 in May and did not feature at all last season after going unsigned following one-year spells with the New York Jets, Buffalo Bills and Miami Dolphins.
Prior to that, Gore played for the Indianapolis Colts after spending nine years in San Francisco, where he was selected as a third-round draft pick in 2005 after moving on from the Miami Hurricanes.
Gore, who has the third-most rushing yards in NFL history (16,000), expressed his desire to end his career with the 49ers as he intends to retire before taking up a staff role working for the franchise.
"Probably in a couple months," Gore told 49ers podcast TheSFNiners. "We're still trying to figure out when I'm going to do my one-day contract, to sign, do my retirement.
"I told [49ers chief executive] Jed York that I always wanted to be a Niner. So we're working on that right now, and then we're going to also sit down with me and my agent to talk about me working in the front office.
"I love looking at talent. I love evaluating talent, and I love ball. And they know that I know football players, what it's supposed to take to be a football player."
Gore became the third player to reach 16,000 rushing yards on Sunday as the Jets claimed their second successive win, defeating the Cleveland Browns 23-16 at MetLife Stadium.
Emmitt Smith and Walter Payton are the only other players to reach that milestone.
The 2020 campaign marked the 37-year-old's 16th season in the NFL but it is unclear whether a Hall-of-Fame career will stretch into year number 17.
"He may try to play again, I'm not sure," Gase told the media on Monday. "As far as what he's done this year, he's helped keep the guys together.
"He's been great with the young players, they've seen him work and understand that no matter what the record is this is how you're supposed to come to work and play the game. I can't say enough of his leading by example."
Gore, who spent his first 10 seasons with the San Francisco 49ers, has previously stated his desire to retire as a member of the Niners, who drafted him in the third round in 2005.
He topped 1,000 rushing yards in eight of his 10 seasons in San Francisco, playing in the NFC Championship game in three successive seasons from 2011 to 2013. He was part of the 49ers team that lost Super Bowl XLVII to the Baltimore Ravens at the end of the 2012 season.
A five-time Pro Bowler and member of the 2010s All-Decade team, Gore holds the record for the most games played by a running back with 241.
In addition to his 16,000 yards on the ground, Gore, who has also played for the Miami Dolphins, Indianapolis Colts and Buffalo Bills, has 81 rushing touchdowns, as well as 484 receptions for 3,985 yards and 18 touchdowns.
