Arter has signed a new three-year deal at the club and claims they have the potential to build on last season's successful survival bid.
Arter, who just missed out on a place in Ireland's squad for their Euro 2016 campaign, signed a new three-year deal with the club on Tuesday, having already spent six years at the Vitality Stadium since his arrival from non-league side Woking in 2010.
Bournemouth manager Eddie Howe enjoyed a successful first season in the Premier League
The Irishman has been a big part of the Cherries' meteoric rise to the Premier League, making a strong contribution to their successful survival bid last season.
And having been a part of two successful promotion bids and two club-record finishes, the 26-year-old says there is no reason why the south-coast outfit cannot build on their impressive first season in the top flight.
He told afcb.co.uk: "The club is going in the right direction and is in the Premier League, where every club wants to play.
"I have been at the club for so long, it’s been a great journey for me and its still going on. We still have a long way to go and I feel we can push on and achieve even more."
Bournemouth's Harry Arter in action with Stoke City's Xherdan Shaqiri
Despite such optimism, Eddie Howe's men are still likely to be among the favourites for the drop next season, but Arter insists the team has the potential to challenge for a top-half finish.
"To get promoted to the Premier League was probably one of the biggest achievements the club will ever have, so if we did finish top half, I think this club is definitely capable of that and it wouldn’t be the biggest shock.
“We can definitely aim to be in the top half and see where that takes us."