Cloning Character For 3D Model Gui Help?

Your problem here is that you're trying to clone and move something from the client. That is not possible. What you might want to consider is creating a RemoteEvent in Workspace and firing it to do the cloning work. So basically keep this in the LocalScript:

local pl = game.Players.LocalPlayer 

if pl and pl.Character then 
    local c = pl.Character
    workspace.RemoteEvent:FireServer(c) -- You can change "RemoteEvent" to whatever your RemoteEvent is called.
    c.Archivable = true
    local duplicate = c:clone()
    duplicate.Parent = game.ReplicatedStorage.NPC
end

game.Players.LocalPlayer.PlayerGui:WaitForChild('PlayerAppear').Enabled = true
game.Players.LocalPlayer.PlayerGui:WaitForChild('PlayerAppear'):WaitForChild('LocalScript').Disabled = false

Now put this inside a ServerScript in Workspace:

workspace.RemoteEvent.OnServerEvent:connect(function(c)
    c.Archivable = true
    local duplicate = c:clone() 
    duplicate.Parent = game.ReplicatedStorage.NPC
end)

Then everything should work as expected.

EDIT:

Since I'm pretty sure you cannot simply clone a player character try this inside the ServerScript:

workspace.RemoteEvent.OnServerEvent:connect(function(plr, c)
    local duplicate = Instance.new("Model")
    duplicate.Name = c.Name
    for _, v in pairs(c:GetChildren()) do
        v:Clone().Parent = duplicate
    end
    duplicate.Parent = game.ReplicatedStorage.NPC
end)