Hi Toby,
Welcome to the world of woodturning.
Regarding getting a tailstock mounted chuck for your lathe, I would echo the comments of Graham and Julcle of saving your money but I will give an additional reason.
The Clarke lathe bed is made from hollow steel bar, and the motor housing from quite thin steel, which means the whole lathe flexes as you apply any pressure by way of the tailstock. In addition, most of them are not particularly well made so there is a lot of lateral movement in the tailstock. This means a drill mounted in the tailstock is unlikely to be on the centre line of the lathe. That results in holes that are bigger than the drill diameter, or worse still, snapped drill bits, as happened with one of my students.
If you need to drill a hole, there is a technique of holding a drill in place manually but explaining all that here would make this post rather long winded. If you want me to send you details, send me a personal message and I can send some pictures etc.
In the meantime, I would save your money and run (turn) with what you've got, then spend your money on a better lathe and accessories in the future.
