Hi Tang,
If I was in your situation, I would get all signed up with your new Agent in the interim and have all advertising ready for the handover.
If you live near the property, arrange for the outgoing inspection to be completed on the last day of their lease. Arrange to attend the inspection and ask your current agent to bring all sets of keys and any relevant information so you can do the complete handover on the day. You will also be able to see with your own eyes the condition of the property and sign off to return the tenants bond on the spot.
That way you know there will be nothing outstanding and you can start with your new agent on a clean slate.
The only down side is that you may have an extra week or so of vacancy as the property won't be shown prior to the tenants vacating.
Hope this helps!