Clement has made an impact since taking charge of the club last month, winning five of his opening six games in all competitions.
His Rangers team beat Sparta Prague 2-1 at Ibrox on Thursday night to boost their chances of being in the knockout rounds of the Europa League this season.
Rangers are playing better football under the Belgian and the fans are connecting with the team again.
Thompson believes the biggest difference between Beale and Clement has been the pace at which Rangers are getting the ball and the bodies forward.
He admitted that while the football was more laborious and slower under the previous manager, Clement’s team are faster and give less time to opposition defences to reorganise themselves.
The former Rangers star said on BBC Radio Scotland: “The way Rangers are playing and the speed at which they are trying to get the ball through the third from back to front.
“More often than not it was one of the full-backs who was passing it up to the wide players, whereas beforehand they would have passed it up, knocked it into midfield, kept it for 10 or 15 passes, allow the defence to get into shape and then go out to a Barisic or a Tavernier to cross it.
“But now the defences they are playing against are not getting the time or the luxury to get into shape because they are moving the ball so much quicker.
“That’s for me has been such a notable change from Michael Beale was here to under Philippe Clement – it’s the speed at which they get up the pitch and it’s not laboured, which it did look towards the end of Michael Beale’s time.”
Rangers will now look to gun down Celtic’s lead at the top of the Scottish Premiership table and will take an away trip to Livingston on Sunday.
