I hadn't thought about a key, thank you.
The problem is a little more complex though. Having got the lathe as a box of bits, I 'think' that originally the gear wheel was also cast iron and part of the sleeve. for some reason the wheel has broken and this is an attempt by someone to repair it. The wheel is only bored out for 3 or 4 mm just enough for a register. If I machine the wheel all the way through to accept a key, I think that it will leave the sleeve too short. There is a triple pulley to fit on the other end of the sleeve.
Last resort I think will be to make a new sleeve and wheel in one piece.
David