According to Apple, Private Relay is expected to work with VPN-based apps, so 1Blocker's in-app tracking filter and Private Relay will likely run alongside without any issues on your device.
However, we've noticed that Private Relay may also conflict with such tools sometimes. For instance, it can stop working if 1Blocker's VPN profile or another VPN is enabled. So, if you activate it and Private Relay still appears enabled in settings, everything should be fine. The problem is that no documentation would explain their interaction in detail, so the best way to check if they can run simultaneously on your device is by enabling them both.
The good news is that the in-app blocking tool already partially covers Private Relay's functionality by preventing app trackers from collecting personal data and sending it to remote servers.
Also, if you have to opt for Apple's tool over 1Blocker's in-app filter for some reason, all the perks of content blocking in Safari, including YouTube ad-blocking, are still available to you as Safari content blocking is handled by a different set of mechanisms.