Advice on turning a part

[Neale]

For the pinion, the hole is probably a nominal 12.7mm - or half-inch as us old-timers know it! Easy enough (but not necessarily very cheap) to get a reamer for that. Biggest issue is maintaining concentricy. Personally, I would hold it by the teeth in a collet. You can make a one-off collet which will be very accurate even if you only have a tired 3-jaw chuck. A drill to open out the hole might work but a small boring tool would be better, whether or not you use a reamer for final sizing.

From what I can see, the shaft is more difficult. Even if it's not hardened, I'm not sure how you will hold it for turning which you will need to do before cutting the thread Possibly another home-made collet would do. Assuming it's just for a securing nut rather than an accurate location surface, a die would do the threading job but there will be a groove between existing thread and shoulder that might give a problem. If it is hardened - make another one from scratch?

[EddyCurrent]

Easy enough (but not necessarily very cheap) to get a reamer for that. Biggest issue is maintaining concentricy.

You are correct, but I was thinking of a morse taper reamer held in the tailstock, same with the drill.
I can't believe I didn't realise it was 1/2", damn mm have warped my brain.

[Neale]

Problem is holding the pinion concentric. With a worn three-jaw, plus locating on teeth, the hole is unlikely to end up in the middle. A home-made split collet can fix that. And a worn lathe probably doesn't have an accurately set tailstock, hence suggestion of a boring tool. It's easy to start over-complicating, isn't it? It's what I would do, but I have the tools to hand. There are probably folks out there who would hand-hold the pinion and use a drill press (but please, don't try that one at home...)