If you add a computer to an AD group that is assigned to a GPO, you need to restart the computer to get the new group membership.
If you want to bypass this, you can delete the Kerberos ticket.
Run the following command as an admin to do this:
klist -li 0x3e7 purge
Et voila, your computer get its new membership!
After that you can run a gpupdate to apply the assgined Policies.