Attempt index with 'stats' in local script StarterGui?

This happens because you probably didn't pass the player argument. There are 2 ways you can do this.

Solution 1

Fixed ServerScript:

game.ReplicatedStorage.NoticeRecall:FireClient(player, player)

The first argument is the player you want to fire the RemoteEvent to, and the 2, 3, 4, etc. are just arguments you want to pass which the 2nd is the player.

Note that the 1st argument isn't passed on to OnClientEvent.

Solution 2

Another way of doing this is not to pass a player argument, but to define the LocalPlayer in the LocalScript which I'd prefer.

ServerScript

game.ReplicatedStorage.NoticeRecall:FireClient(player)

LocalScript

local client = game.Players.LocalPlayer

game.ReplicatedStorage.NoticeRecall.OnClientEvent:Connect(function()

    local leaderstats = client.stats
    local gold = leaderstats.Stolen

    local frame = script.Parent.Frame
    local text = frame.Label
    frame.Visible = true
    text.Text = "You received: "..gold
    wait(5)
    frame.Visible = false
end)

You can see the :FireClient() parameters here.