Why isnt this working? (Very short and easy code, and its in a localscript)

script.Parent.ClickDetector.MouseClick:connect(function(p)
    local Torso = p.Character:WaitForChild("Torso")

    Torso.Anchored = true
        if p.Backpack:findFirstChild("Fish") then
            p.Backpack:findFirstChild("Fish").Handle.Mesh.VertexColor = Vector3.new(0.4,0.4,0.4)
        wait(2)
        Torso.Anchored = false
    end
end)

I'm not sure why you were trying to use LocalPlayer when MouseClick returns the player?

When the MouseClick event is fired, it gives the player who clicked as an argument, in this case 'p.'

Try this.

script.Parent.ClickDetector.MouseClick:connect(function(p)
    if p.Character then -- Checks if the players character isn't nil
        local torso = p.Character:FindFirstChild("Torso")
        local fish = p.Backpack:FindFirstChild("Fish")

        if torso then -- if torso exists
                torso.Anchored = true

                if fish then -- if fish exists
                    p.Backpack.Fish.Handle.Mesh.VertexColor = Vector3.new(0.4,0.4,0.4)
                    wait(2)
                end

                torso.Anchored = false
        end
    end
end)