It is likely that the spindle has a Morse taper in the bore. I have a D1-3 nose on my Colchester Bantam and this has a MT5 taper. If yours does have a Morse taper, you can buy a collet chuck eg ER32 or ER40. You will need a drawbar too but that should be simple to make.

These are widely available on ebay, Amazon and AliExpress
https://www.aliexpress.com/item/32908168694.html