Valorant error code VAL 59 occurs during the login queue process, which essentially means that you were unable to connect to Valorant servers after launching the game. Try the following methods to fix the error.

Restart Valorant
After restarting the Valorant client, the error code should usually be resolved. After restarting the Valorant client, you should also exit the Riot launcher and then restart the Valorant client again.
Related: How to Get Account Points (AP) in Valorant | GF: Guide Me!
Restart Your PC
Occasionally, a simple restart of Valorant may not be sufficient to solve the issue. If that is the case, reboot your PC from scratch in order to resolve the issue.
Restart Your Internet Connection
Try unplugging your modem/router for at least 30 seconds, then reconnecting them if this doesn’t work. If rebooting Valorant and your PC doesn’t work, try refreshing your internet connection.
Reinstall Riot Vanguard
If none of the previous methods work, it may be necessary to reinstall Riot’s anti-cheat software, Vanguard. To do this, select the Vanguard entry in the list of installed programs in Windows and select Uninstall.
Submit a Support Ticket
In case all else fails, you can always contact Riot Support via their official support page. From there, you can browse through commonly asked questions or submit a ticket directly.
Related: Valorant: How to Fix ‘Could Not Enter Matchmaking’ Error – Stop Making Excuses!