You need to update the Wi-fi settings on the stick to the new router. See this link which should point you in the right direction.
Go into the Stick Settings under Network, change wireless connection and select your Network id shown and then enter your Router Wi-Fi password.
To reach Settings on the NOW Stick, keep pressing the back button on remote from the NOW home screen until you see a hidden menu on the left-hand side of the TV screen which includes Settings.
If you can't see your Network ID name under change wireless settings, then change the Wi-Fi channel on your Router to one of the lower channel numbers.
Alternatively, set the new router to have the same SSID and password as your previous one, and all your existing WiFi devices will instantly connect without you having to change each one individually.
Don’t raise the devices ‘bridge’ when you can lower the router ‘river’ 😛