Arteta ended the club's 22-year wait for a Premier League title in May and has extended his contract to 2030.
The club also reached the Champions League final, losing on penalties to PSG, and posted club-record revenue. Garlick said, however, they were not resting on their laurels as they seek to build on a stellar campaign on and off the pitch.
"We can't stand still. We can't sit there, pat ourselves on the back, and say job done. This is the beginning, not the end of our journey. This is where we want to go on and show the confidence that that win is going to bring to us," Garlick said at the Leaders Week sports industry conference at Stamford Bridge.
"We want to dominate football for the next number of years. We're in a really strong position to do that, but... we need to keep finding that edge that gives us that advantage, and we have to be brave because it'd be very easy just to simply say 'we'll just roll over what we did last year, and that'll be enough', because everybody's out to get you.
"When you're champions, everybody wants to beat you, and we need to find a way of taking those opportunities and taking those advantages and pushing forward all the time."
Arsenal were ranked seventh in the 2026 Deloitte money league for the world's top revenue-generating clubs, behind Manchester City.
However, with City being found guilty of all charges relating to breaches of the Premier League's financial rules from 2009-10 to 2017-18, there may be a gap to exploit in English football. City have appealed the league's decision and continue to deny wrongdoing.
Faith in Arteta
Arsenal, owned by American company Kroenke Sports & Entertainment, will be helped by club-record revenue of 822 million euros ($918.91 million) in 2025, a 15% increase from the previous year and more expected this year.
With Arteta's mentor Pep Guardiola having left City in the close season, the Arsenal manager is now the longest-serving manager in the league after joining in December 2019.
Garlick sees that faith in Arteta, who struggled early on in his tenure, as key to Arsenal's growing success.
"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.
"You look at all the other teams in the sort of traditional top six, and they've all gone through managerial changes... whereas 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.
"And the excitement now is we see (the) platform that we've got and we build from there."
Arsenal are second in the Premier League standings with 12 points from five games and host Leeds United on Saturday.