*** Please read the permissions and caveats sections below before leaving a negative review! *** The existing add-ons I found for replacing the new tab URL emulate the `browser.newtab.url` functionality of Firefox <41 that change the address bar to a specific URL. This add-on lets you set a custom URL without changing the address bar content so the cursor remains focused in the address bar and you can just start typing to search or navigate to a different URL. Instructions To set your custom new tab URL after installing the extension:

Open `Add-ons` from the `Menu (☰)` (or navigate to `about:addons` with the address bar)
Select `Extensions`
Select the `Custom New Tab Page` extension → `Options`
Enter your URL in the `New Tab URL` box
Press `Save`
Done!

Permissions Please note the "Access your data for all websites" permission is completely optional and only required if you enable advanced options. Even when advanced options are enabled, the add-on will only ask to access data for the site configured as your new tab page. Core functionality of this add-on will work without granting any extra permissions. Caveats

Only http:// and https:// URLs are currently supported. Due to security restrictions imposed by Mozilla, local file:// URLs will NOT work.
Links on the site you choose will open in the iframe (issue #1). If you control the site add target="_top" to the links to make them open in the top frame.

If you're looking for a new new-tab page then check out my site Zen.