"Can we improve this script by making the camerapart follow the player so that the camera isn't fixed at the location of the part but still stays with the player?"

Yes, we can improve the script by making the cameraPart follow the player. Here's how you can do it:

```lua
-- Local script 
local player = game.Players.LocalPlayer
local UserInputService = game:GetService("UserInputService")
local camera = workspace.CurrentCamera
local zoomedIn = false
local defaultFieldOfView = 70
local zoomedFieldOfView = 20
local zoomOffset = Vector3.new(0, 2, 0) -- this is the offset value when zoomed in

-- Create an invisible part for the camera to follow
local cameraPart = Instance.new("Part")
cameraPart.Transparency = 1
cameraPart.CanCollide = false
cameraPart.Anchored = true
cameraPart.Parent = workspace

-- Create a function to update the camera part's position
local function updateCameraPart()
    if zoomedIn then
        cameraPart.Position = player.Character.HumanoidRootPart.Position + zoomOffset -- move the camera part
    end
end

-- Connect the function to the RenderStepped event
game:GetService("RunService").RenderStepped:Connect(updateCameraPart)

UserInputService.InputBegan:Connect(function(input)
    if input.KeyCode == Enum.KeyCode.Z then
        if zoomedIn then
            camera.FieldOfView = defaultFieldOfView
            camera.CameraSubject = player.Character.Humanoid -- set the camera to follow the player
            zoomedIn = false
        else
            camera.FieldOfView = zoomedFieldOfView
            camera.CameraSubject = cameraPart -- set the camera to follow the camera part
            zoomedIn = true
        end
    end
end)
```

In this script, we added a function `updateCameraPart` to update the position of the camera part. We connected this function to the `RenderStepped` event, which fires every time a frame is rendered. This will make the camera part follow the player when zoomed in.