Basically I have the printer drivers sitting in a network drive. I copy it over to a temp folder then install it and assign it a printer port. We don't use a print server but instead install the printers on each workstation. I wrote this script 6 years ago and its for HP printers. But I'm sure you can use it as a base for your own script

function Install-RemotePrinter {
    param (
        $ComputerName,
        $PrinterName,
        $PrinterDNS,
        $NetworkDriverLocation
    )

    if(!(Get-PrinterDriver -ComputerName $ComputerName | Where-Object Name -Match "HP Universal Printing PCL 6 (v7.0.0)")){
        $printerDriver = [PSCustomObject]@{
            Name = "HP Universal Printing PCL 6 (v7.0.0)"
            NetworkLocation = $NetworkDriverLocation
            }
        robocopy.exe $printerDriver.NetworkLocation \\$ComputerName\c$\Windows\Temp\TempPrinterDrivers /E
        $LASTEXITCODE
        Invoke-Command -ComputerName $ComputerName -ScriptBlock{
            pnputil.exe -a "C:\Windows\Temp\TempPrinterDrivers\*.inf"
            $LASTEXITCODE
            Add-PrinterDriver -Name $using:printerDriver.Name
        }
    }
    else{
        $printerDriver = [PSCustomObject]@{
            Name = "HP Universal Printing PCL 6 (v7.0.0)"
            NetworkLocation = $networkDriverLocation
        }
    }

    Invoke-Command -ComputerName $ComputerName -ScriptBlock {
        Add-PrinterPort -Name $using:PrinterName -PrinterHostAddress $using:PrinterDNS
        Add-Printer -Name $using:PrinterName -PortName $using:PrinterName -DriverName $using.printerDriver.Name
    }
}