What is going to be the best way to do this?
Should I set up a new Ltd company/Amazon Account for that brand to keep the two separate or should I just apply for a new brand registry under my current PL brand/company?
You do not need a separate Amazon account or company to run a second brand. Amazon allows multiple brands under one seller account and you can apply for Brand Registry for each brand separately as long as each one has its own registered trademark. Keeping both under one account actually makes things easier to manage since you have one dashboard, one billing and one performance history. A separate Ltd company only makes sense if you are planning to bring in partners, investors or sell one of the brands independently down the line as a standalone business asset. For most sellers starting a second brand just register the new trademark, apply for Brand Registry under the same account and keep things simple.
Are you planning to sell in the same category as your first brand or going into a completely different niche?
I run two brands under one Ltd, much easier for accounting. Just file a new trademark and register it under your existing Brand Registry. Saves you from managing two Seller Central accounts. Happy to share how I structured my listings if you need.