Some issues with your initial script
First
Get-AdUser won't give you the property Department by default.
You could have confirmed this by actually looking at the output of your Get-AdUser statement. You do need to add it to the list of properties explicitely.
get-Aduser -f {GivenName -eq 'Jack'} -Properties Department
Also, you did make a mistake in the Set-AdUser cmdlet. The parameter name you have written, at the time of my answer, is -departement. Instead, you need to set -department.
Finally, Get-AdUser could return multiple users (or none).
Therefore, you need to account for that by checking how many $member were returned or to do a foreach to process none (if 0) or all of them the same.
At least, that part is subjective to what you need but here would be my approach.
$member = get-Aduser -Filter 'GivenName -like "Jack*"' -Properties Department
$member | foreach {
if ($member.Department -eq 'Dep20')
{
$_.Department = 'Dep21'
set-AdUser $_ -Department $_.Department;
}
}
Edit:
I modified my answer to switch the Filter parameter from a scriptblock (as your question) for a string filter as per mklement0 comment.
Because the Filter parameter is actually a string, giving it a script block will create problems on multiple occasions and you are better restrict yourself to the string type for this parameter.
See this for a more detailed explanation on the matter.