Mikel Arteta ended Arsenal's 22-year wait for the Premier League title in May and has now committed his future to the club until 2030. Arsenal also reached the UEFA Champions League final last season, where they lost to Paris Saint-Germain on penalties.
Garlick insists the club cannot afford to become complacent after a record-breaking campaign.
"We can't stand still. We can't sit there, pat ourselves on the back, and say job done," Garlick said at the Leaders Week sports industry conference at Stamford Bridge.
"This is the beginning, not the end of our journey."
Arsenal also recorded club-record revenue of 822 million euros in 2025, an increase of 15 per cent from the previous year, strengthening their position among Europe's biggest clubs.
Garlick believes Arsenal now have the foundations to challenge for major honours consistently, but warned that maintaining their advantage will require continued ambition.
"We want to dominate football for the next number of years," he said. "We're in a really strong position to do that, but we need to keep finding that edge that gives us that advantage."
The Arsenal chief also highlighted Arteta's long tenure as a major advantage. The Spaniard joined the club in December 2019 and is now the Premier League's longest-serving manager following Pep Guardiola's departure from Manchester City.
"I think it gives us a competitive advantage over the other teams because Mikel is the only manager that's won the Premier League that's currently managing," Garlick said.
While other leading clubs have gone through managerial changes, Arteta has been given time to develop Arsenal's squad and establish his footballing philosophy.
"You look at all the other teams in the traditional top six, and they've all gone through managerial changes," Garlick added.
"We've now got a manager who's been with us for a significant period of time and has been allowed to build and develop a team over a period of time."
Arsenal currently sit second in the Premier League with 12 points from five matches and host Leeds United on Saturday as they look to build on their title-winning campaign.
