Hi There,
We went through this same process last December with AIB so unless things have changed since then I have a very good idea of the process.
We sold and bought the same day. So closed the sale of our existing property in the morning, clearing our old Tracker mortgage and then closed the purchase that afternoon.
The funds for the new mortgage were actually with our solicitor a couple of days before we closed our sale, ensuring then we could complete both on the same day.
At the time AIB also advised me that we could sell, clear our existing mortgage and then avail of the tracker mover mortgage within a "reasonable" time frame after that. This was to allow for the instance that we had sold and our new home wasn't ready in time.
Hope that helps!