Yes, if you have the tesla charging cable, the Teslatap will attach to that and allow you to then charge using your existing setup. You will notice some differences in how they function, however. With your Tesla, if you have that car programmed to charge during specific time periods in order to take advantage of your electric company's discounted off-peak rates, when you plug into the Tesla, it knows to wait until the specified start time. With the Jaguar using the Teslatap, it will immediately begin to charge once you plug in - even if you have set the car or the app to charge only during certain time periods. If you want the Jaguar to charge only during those periods, after you plug in and it begins to charge, you must go to your app and pause it. Once paused it will then begin to charge again during the times you have programmed. You have to do this EVERY time you plug in.
If you want to avoid this, or no longer have the Tesla cable, you can get a programmable charger that WILL sync with the car and only charge during the programed time frames. I have a Juicebox Pro, but the ChargePoint system will do the same.
Another advantage of the Teslatap is that it will allow you to charge at Tesla destination chargers (but not Super Chargers).
I hope all of that was clear. Although I LOVE the Jaguar, you will find that the Tesla charging system is vastly superior.