(Pasted from this YouTube video as it may be helpful, https://youtu.be/a2GYYyNVEHg)

It's a remastered and extended version you can find in the third limited extra disc of the 20th anniversary album of the soundtrack, you can check the information here:

https://vgmdb.net/album/84708

It was originally composed by Kohta Takahashi, and remastered by Shinji Hosoe.
I couldn't find it on SoundCloud, so here it is.

 You can find and download it here, along with the entire soundtrack and remixes:

https://downloads.khinsider.com/game-soundtracks/album/r4-ridge-racer-type-4-the-20th-anniv.-sounds-extra-disc/3-06%2520Move%2520Me.mp3

R4 Ridge Racer Type 4 - Move Me (20th Anniversary Remaster)

Main: @ScoredBuffalo31
Yo. I just upload whatever I like if I can so I can have it play in the background, or to let others listen if it's not here. All of what's uploaded here isn't mine and credits go to their respective creators and owners if possible (check the descriptions!). I'm not making any money off of this either.

If anything needs to be taken down, DM me through my Twitter, @ScoredBuffalo31. You'll most likely get a response from me there. You can also now message me on SoundCloud, so there's that as well.

R4 Ridge Racer Type 4 - Move Me (20th Anniversary Remaster)

Scored31