My Apple TV Remote (A1513) won't pair to my Apple TV (A1625)

Apple TV Remote (A1513), Apple TV (A1625)

That would be the black Siri Remote, without the white ring around the Menu button. That seems original to the model Apple TV box HD (4th generation) for some time.

I have tried everything that I found on the Apple website and I couldn't pair my remote. I have brought it SH and the Apple TV works perfectly but the problem is my remote, I have charged it for a total of like 2 hours to be sure it isn't that, I have tried the pair setup and getting very close to the Apple TV, tried resetting and nothing worked.

While you wouldn’t know the care that was taken for second hand accessories, let’s assume for now that this remote is in good order to be functional. If it is broken or damaged internally, then you’ll have to replace it. Later models remotes are also compatible (if the system software is version 15.4 or later).

If your Siri Remote or Apple TV Remote isn't working - Apple Support

• To charge the remote, connect it via Lightning-to-USB cable to a computer, or to a USB power adapter in an AC socket. Other USB connections may not be suitable for this. Charge for at least 30 mins to have enough juice (~60%) for use at that moment. Charge for up to 2.5–3 hours for 100% charge level.
• To pair the Siri Remote to an Apple TV box, press the Menu button and Volume Up button simultaneously, for up to 5 seconds. A message should then appear on-screen, telling you it has detected the remote and that it succeeded in pairing, or to bring it closer to the box. If there is bluetooth interference, then the ultimate closeness is to lay the remote on top of the box.
• Apple TV Remote (A1513) is compatible with all current models Apple TV (excluding the legacy models A1469 and earlier), regardless of version system software.

If the remote battery is just too old (too many charge cycles) and won’t keep charge anymore (possible for a 2015 unit), then you can contact Apple about battery service. If it turns out that the battery was indeed the cause, then you would be eligible for a replacement remote at discount price ($29 instead of $59). Apple TV repair and service - Apple Support