Welcome to the forum Tina, tell us about yourself in the 'Introduce Yourself' department and show us some pictures of your lathe so that we can get an idea of what you mean although I'm sure the wrinklies will understand.
Hi Tina, what lathe do you have?
Peter
if the spindle is 3/4" x 16tpi then yoy could use an Axy junior collet chuck with a 6-7mm collet Axminster Junior Chuck - Woodturners Chucks - Woodturners Chucks - Woodturning - Woodturning & Crafts | Axminster Tools & Machinery and a mandrel shaft and if you have a hollow tailstock then you would probably need a mandrel saver Axminster Evolution Series Quick Change Pen Centre - Live Tailstock Centres - Lathe Accessories - Woodturning - Woodturning & Crafts | Axminster Tools & Machinery
Hi Tina, all the suggestions above should sort you out for pen making, but if you do need a Morse taper for anything else you could always use a Morse taper carrier like this Axminster one in your chuck. Just make sure you get one that is designed for your make of chuck.