Clement has been rebuilding his squad, with experienced players Connor Goldson, Ryan Jack, Borna Barisic, John Lundstram, Sam Lammers and Kemar Roofe among the summer departures.
Connor Barron, Vaclav Cerny, Jefte, Clinton Nsiala and Robin Propper are among the new players recruited so far in the summer window.
Rangers kick off their Premiership campaign away to Hearts on Saturday at 12:30 BST.
And Clement said: “I’m 200% sure we’re going to be much better in October and November, December and the months coming after.
“It’s a squad with a lot of potential, more potential than there was last season.
“We’re not there yet. The way we want to play, it’s in a structured way – with the ball and without the ball.”
Commenting on the new contract, chairman John Bennett told Rangers’ website: “Philippe and I had a far-reaching conversation at the end of May.
“Our shared ambition was clear: the rebuild of the Rangers men’s first team for the long term as well as short term.
“At that meeting we shook hands on this new contract and the board is delighted that the formalities have been concluded.”
