I'm looking for an app that would replicate Garmin's virtual partner (= race against your previous record), but on my phone as I don't feel like using a dedicated device.
That would be for outdoor cycling.
Ideally, I'm looking for a solution where you constantly see if you are ahead or behind your previous record.
If the app is free, that's even better.

Thanks

For indoor cycling or outdoors in the real world? Might make a difference for what recommendations you get. I don't know of anything for outdoor cycling. I don't use it on my Garmin. And they are rarely discussed here.

This didn't quite click with me how you meant it. I can make it work either way depending on how I read it related to the sentence in the previous line.

Yeah, it would be for outdoor.
The idea is to ride with a different color on the screen depending if you are ahead or behind your best time, so you just need to stay slightly ahead to beat your record.

Strava might be worth looking at.