I just installed my new router. SSID and password is the same as precious.
How do I add my ST hub to my router without resetting everything?
Which model hub?
It’s the ST v3
You shouldn’t have to reset anything, you’re just going to change your Wi-Fi credentials. Basically the same thing you do with your phone or your Xbox or anything else that connects to your Wi-Fi. 
See the instructions in the support article section on changing the Wi-Fi network.
https://support.smartthings.com/hc/en-us/articles/115002084806-How-to-add-a-SmartThings-Hub-
Note: Changing the Wi-Fi network that the SmartThings Hub is connected to will not affect any existing devices, Scenes, or Automations.