Options for replacing a 7 speed Shimano cassette / chain I would like to replace my 7 speed HG70 cassette and chain. My problem is that it is increasingly difficult to find quality parts for 7 speed system.

My bike is a Trek 970 from 1993, originally with Deore XT / DX system.

Last time I changed I could bought a 7 speed HG70 12-28 cassette and a HG70 chain, but now these are super rare and are only possible to find on eBay for NOS prices.

What I would like to ask is that what are the exact steps and parts I need to change if I would like to upgrade for an 8 of 9 system, as mentioned by Sheldon Brown? Other than buying a 9 speed cassette, a 9 speed chain and a 9 speed rear shifter, what do I need to buy or fix?
You don't need to buy NOS. 7 speed cassettes are still manufactured, we stock them and they start at $20 all the way up to $36 for a Shimano HG50 which comes in 12-28. Go with a matching Shimano HG50 chain.

Unless you buy a new rear wheel, you cannot go above 7 speed. 7 speed freehub bodies are shorter than 8+ speed freehub bodies. An 8+ speed cassette is too wide to fit your freehub.