To do this you need to use the Text tool itself, not the Move tool.
Click the Text tool at the tip of the existing leader arrow … and if you’re in luck, it grabs the arrow, while it automatically changes to the Move tool.
It’s a fiddly maneuver that doesn’t always work the first time, or the second time, or the third…
When it fails to work, hit Escape and try again. Orbiting to get a different view tends to help.
I find it’s easier/quicker to edit the existing text and copy all of it to the clipboard.
Then create a new Text entity and simply paste in the text from the clipboard.
Erase the old one when finished.