Log in to BA.com ... click on manage my account and on the left side you will see a menu with "Executive club items" near the bottom of the list
For me, clicking on that shows that my tier point year that expired April 8 with a card ending May 31st, the new card was dispatched to me on April 26th. The first entry marked "pending" was from April 15th
So around now you should be able to start to monitor the status of your new card in the same way and based on my experience you should see the card dispatched around the end the end of September