Click-part GUI won't pop up?

MainScreen is declared twice. No reason to do that.

MainScreen:Clone() is a function that returns the cloned object. To use :Clone() properly, you would declare another variable as MainScreen:Clone().

You're moving the original MainScreen into the player's PlayerGui. Move the clone instead.

Fixed script:

--Variables
MainScreen = script.Parent.GUI.CardGiverGui
XButton = script.Parent.GUI.CardGiverGui.Main.X

function onClicked()
    local screenClone = MainScreen:Clone()
    screenClone.Parent = game.Players.LocalPlayer.PlayerGui
end

So, all guis need to run on the client, great, local script! but wait, ClickDetectors don't work on a local script, only on a server script

How do we fix this?

We use a little thing called Remote events

What's a remote event?

For a short description, it basically sends stuff to the other side, useful for FE games.

So, in ReplicatedStorage, insert a RemoteEvent, name it whatever you want, and in a local script where you will manage the gui,

--LOCAL SCRIPT
local plr = game.Players.LocalPlayer --so we can get the plrgui easier,
local gui = --post where it is

game.ReplicatedStorage.RemoteEvent.OnClientEvent:Connect(function()
--We are waiting until the server script fires this, when it does it will run

--Now we should move the gui into the player Gui
--if you want to clone it, then here
local new = gui:Clone()
new.Parent = plr.PlayerGui

--If it's already in plrgui, then just make it visible (if it's not)
gui.Visible = not gui.Visible
end)

Now, we shall fire this client event through the server script

--SERVER SCRIPT

local cd = --post where the click detector is
local re = game.ReplicatedStorage.RemoteEvent 

cd.OnClicked:Connect(function(player) --I don't actually know what event it has, my bad if its wrong
--If you don't know, I am doing an anonymous function, basically without a name.
    re:FireClient(player)
end)

I HAVE NOT TESTED THIS IN STUDIO, I DON'T KNOW IF ANYTHING WILL ERROR

Hope this helps! If it does, make sure to accept this answer! If not, please comment what's wrong and I'll try my best to fix it!

Any other concerns, or comments, make sure to post below and I'll try my best to answer!

-John