The left back penned a new five-year deal on Thursday following the arrival of the former Swansea defender and believes the competition will improve both players this season.
Rose penned a new five-year deal at White Hart Lane on Thursday, extending his stay at White Hart Lane to 2019, after making a career-high 22 Premier League appearances for Spurs last season.
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New head coach Mauricio Pochettino has ensured there will be competition for a left back berth at the north London club by bringing in Davies from Swansea City last month, but Rose is relishing the competition.
"I'm over the moon to sign my new contract," Rose told the club's official website. "I'm glad it's been sorted and now I can focus on the start of the season. Working under Mauricio has been brilliant. We went through our first three games unbeaten [during the U.S. tour] so we're all happy and everyone has a good understanding of what the manager wants to implement.
"We've brought in Ben Davies now and I'm hoping he can improve me, and likewise I'm hoping I can help him settle in and help him improve his game as well. There are two or three good players in each position at the club and we're all excited for the start of the season."
Rose is also hoping he and Tottenham can both show a higher level of consistency in the new season.
He added: "This season, first and foremost, I want to stay injury free. I had a small, annoying injury ... and when I came back I was a bit inconsistent with my performances so I'm determined to improve on.
"From a club point of view I hope we can be a bit more consistent as well because we lost to and drew with teams that we feel we should be beating last season. While this season will be a difficult one, we're all looking forward to it."