Tailstock rotating centre. No.2 Morse taper (appearance may differ from the photograph but the specification is the same).

For a No.1 Morse taper rotating centre see; https://store.lathes.co.uk/parts/tailstock-rotating-centre-no-1-morse-taper

For a No.3 Morse taper rotating centre see: https://store.lathes.co.uk/parts/no-3-morse-taper-rotating-centre