1. to prefer ("A+Acc B+Dat vorziehen" - "bevorzugen" is by far more common in daily life. If at all, "vorziehen" is used in combination with actions, not things, so the phrasing is often "ich ziehe es vor, ... zu ...")
2. move ahead (ONLY for rescheduling meetings and appointments.)
3. pull to the front ("hervorziehen" and "nach vorne ziehen" are more common here)