You must send “continue taxi at your discretion” after sending the final progressive taxi instruction, per the ATC manual. It’s a major thing I see constantly with new ATC trainees in training.
And you can send the command immediately after the last progressive taxi instruction, you don’t need to wait till they have reached their intended location.
For example, you tell them to “turn right on the next taxiway”, which is a hold short point for a runway. Right after you send that command feel free to send “continue taxi at your discretion” because they must follow the turn right instruction.
References: 5.2.2 of the ATC Manual