Can I make a cloned part from a local script to be sent in the workspace through remote events?

Using a LocalScript will only show it on the Client side. If you want a LocalScript to create a part and then send it to the workspace, you will need to use a RemoteEvent.

Create a Script in ServerScriptService and name it whatever you want. Create a RemoteEvent in ReplicatedStorage and name it whatever. Create the LocalScript wherever that is going to call the Event.

In this example:

Script Name: CreatePart

LocalScript Name: LocalCreatePart

Event Name: CreatePartEvent

In LocalScript:

local Event = game:GetService("ReplicatedStorage"):FindFirstChild("CreatePartEvent")

Event:FireServer()

In Server Script:

local Event = game:GetService("ReplicatedStorage"):FindFirstChild("CreatePartEvent")

Event.OnServerEvent:Connect(function(player)
	local Part = Instance.new("Part")
	Part.Parent = game.Workspace
	Part.Name = "Created Part"

	print(player.Name.." Created a Part in Workspace")
end)

The above will create a Part in Workspace through a LocalScript with the name of Created Part for all players to see.

Please note: RemoteEvents can be exploited. You should be careful where you place your event. Script Executers can find your event if not hidden well.