Below PS script to update a manage metadata column. We can update columnby updating a managed-metadata column. Format of value is  "16;# Warriors" in groupType field.

$weburl="/sites/manager"

$web = Get-SPWeb $webUrl

$list = $web.Lists["department"]

$ct = "Deptgroup"

$f = "groupType" #Column Name      

$newTerm = "10;#test

 Agreement|1273c09f-4ar1-453e-8422-60601d61bd11"

foreach ($item in $list.items)

{

    try {

        If ($item.ContentType.Name -eq $ct)

        {           

            $field = $list.Fields[$f]

            $fieldValue = $item[$f]

            if($fieldValue -eq $null)

            {               

                $item[$field] = $newTerm                

                $item.Update();                     

            }

        } 

        }   

    catch{

        Write-Host $item.Name " error occured" 

        }   

} 

#finally dispose the web

$web.dispose()

#updatelisitems #managedmetadata #columnname