Arteta signed a new four-year agreement on Wednesday after guiding Arsenal to their first Premier League title in 22 years last season.
The Spaniard took charge in 2019 when the club were struggling for consistency and has since overseen a major rebuild of the squad, coaching staff and wider football operation.
Garlick believes that continuity now gives Arsenal an advantage as they attempt to build on their title success and challenge for further honours.
“We can't stand still,” Garlick said. “We can't sit there and pat ourselves on the back and say, 'job done'. This is the beginning and not the end of our journey.”
Arsenal’s chief executive also made clear that the club’s ambition extends beyond their first league title under Arteta.
“We want to dominate football for the next number of years and we are in a really strong position to do that,” he said.
Garlick believes Arteta’s longevity is particularly valuable at a time when several of Arsenal’s traditional rivals have changed managers.
“It gives us a competitive advantage over the other teams,” he said. “We've got a manager who has been allowed to build and develop over time. It's not the end of it, it's an exciting new beginning for us.”
Arteta is now the longest-serving current manager in the Premier League by some distance following Pep Guardiola’s departure from Manchester City last season.
Unai Emery is the next-longest-serving manager, having been at Aston Villa for just under four years.
Garlick pointed to Arteta’s record and stability as another reason Arsenal believe they are well placed for the next stage of their project.
“I look at the other teams in the Premier League and Mikel is now the only current manager that has won the Premier League,” he said at the Leaders Week conference in London.
“You look at the other traditional top-six teams and they have all gone through managerial changes in the past 12 months, whereas we now have a manager who has been with us for a significant period of time.”
Arsenal now hope the new contract can provide the platform for Arteta to turn last season’s title success into a sustained period of domestic dominance. The club see continuity as central to that ambition.