Hide Edge Button in IE11

Open the local Group Policy Editor.

Windows logo keyboard key + R and type gpedit.msc hit enter or click OK.

In the left navigation pane, navigate to:
User Configuration\Administrative Templates\Windows Components/Internet Explorer\Internet Settings\Advanced Settings\Browsing\

In the right data pane locate:

"Hide the button (next to the New Tab button) that opens Microsoft Edge.

Double click it and change it from "Not configured" to "Enabled"

Reboot.

To undo simply switch it back to "Not configured"



OR

If you are running the home version and do not have the Group Policy Editor you can use the Registry Editor:

Windows logo keyboard key + R and type:
regedit

Hit enter or click OK

In the left Navigation pane, navigate to:

HKEY_CURRENT_USER\Software\Policies\Microsoft\Internet Explorer\Main

In the right data pane change the value of "HideNewEdgeButton" from 0 (zero) to 1 (one).

If that particular data value is not present you will have to create a New -> DWORD (32-bit) Value and name it HideNewEdgeButton with a data value of 1 (one).

Reboot.

To undo, simply switch it back from 1 (one) to 0 (zero)