ClickDetector in a gui?

I don't know if it's possible, but it's not necessary. To get the player who clicked the button, all you'd need is the proper Event.

Assuming you want to find the player who clicked your GUI with the left mouse button, just use the MouseButton1Down() or MouseButton1Click events in a localscript. Here's an example:

local GUI = script.Parent --Assume the localscript is located in the GUI Button.

GUI.MouseButton1Click:connect(function(player) --player is the player who clicked it.
    print(player.Name) -- Prints player's name into the output. Remember, this is sample code, so this is just an example.
end)

Hope this helps, and if you have any questions lemme know. :)