A really funny thing you can do with alpha t-rexes is to get a rhynio, lure an alpha t rex to the beach, and get it to swim after you in the ocean. If it loses interest and becomes passive, then get close to it and dismount on your rhynio and it should start swimming after you again. Then when it gets too close you can fly some distance away, dismount, and it will start chasing you again. Do this a few dozen times and you can trick the alpha rex into swimming to herbivore island or any other crazy location since alphas can't drown.

You can also leave the alpha rex at sea then fly away from it until it disappears in your render distance and forget about it since it will never despawn, drown, or even move so you can go to it later to kill it.

Bonus tip: if you dismount on your rhynio, your rhynio will automatically start regenerating stamina in the air after 5 seconds.