The 49-year-old took charge of his first training session on Monday after he was confirmed as the 19th permanent manager of the Light Blues less than seven days ago.
And Tavernier says the Belgian has made a positive impression in his first few days in charge as he looks to imprint his footballing philosophy on the squad.
Speaking to the media ahead of tomorrow's league clash, the captain commented: "It's been really good and positive.
"We've had a few international boys away who have recently joined us, but the young lads have filled their spots in training and it's been good.
"It's still obviously early stages and he's going to try and put his identity on the team. We'll slowly work on it every day and you'll be seeing it when we play.
"It's refreshing and good to see a different aspect about how to play football again. We're all really tuned in to the way that he wants, and we've got to implement it as quickly as possible.
"The manager wants us to win games; he's a winner himself. He wants us to play a certain way while fighting and winning games.
"We already want to do that, but he's raised the standard as soon as he's come in. It's about improving as a team, and as players, and tomorrow is a game that we want to get three points in."
Clement was keen to stress the importance of the supporters earlier this week as he charts what he hopes will be a successful journey for the Light Blues.
Tavernier's own individual journey at Ibrox has led him from the Scottish second tier to the heights of a European final, and the 31-year-old hopes to create more special memories for the supporters to cherish during Clement’s time in charge of the club.
He continued: "I had a good chat with the gaffer and it's a two-way street between ourselves and the fans. I've been here a number of years where we've experienced great moments in the stadium where the fans have been behind us.
"We always want the fans to be behind us whatever the situation that we're in, but we have to give them the performances that they're looking for. I believe both of us together can be very strong.
"You can't dwell on anything as a Rangers player. You can reflect on it and see where you can do better. We all want to push each other as a group and make each player better, and the best way of doing that is coming in every day and trying to get the three points and performance on gameday.
"Tomorrow is about us going on the pitch and giving everything that we want to give a performance the fans want to see."