There may be other options depending on how people setup their PS4, but this is my understanding and way of doing it.
Uploading to Youtube is done via video clips found in the "Capture Gallery" on the PS4's main menu.
So you need to get your game-play video there.
If you have a saved replay in GT Sport you wish to share, then playing the video and recording it is a way to get that video to the Capture Gallery.
Double pressing the Share button begins video recording, and double pressing the Share button ends video recording.
So, in GT Sport, play the saved replay and record it.
This video recording will be exactly as you see it on screen (meaning during recording you can change car views, turn on or off race data, view a different car, etc.) and is saved in the Capture Gallery.
(Note: Turn off HDR in the settings before you start recording to avoid over-saturated colours in the saved video clip)
After that, on the PS4 main menu, go to the Capture Gallery.
Highlighting the video clip and pressing the Share button will allow you to upload to Youtube.
Or you can highlight the video clip and press the Options button which will allow you to "Trim" or "Edit in Sharefactory" before uploading.
*Edit*
I'll also add this.
There may be times when something happens during game-play that you want to share, but you are unable to "save" in GT Sport and then play back.
For example, on track in a lobby but not actually racing to allow a race save.
The PS4 is continuously recording, and will always hold the last 15mins of game-play.
At any time, pressing the Share button once (not double pressed as per before) will allow you to "Save Video Clip".
This video clip will be a recording of the last 15mins of game-play as seen on screen (meaning you can't manipulate it as per before) and will be saved in the Capture Gallery.