Presuming you still maintain your previous citizenship (in addition to your UK citizenship) AND you still have that passport and it’s still valid, then you can travel on that passport/visa. There is no need to apply for a new ESTA or visa, and doing so will only put your current visa status at risk.
When your current visa expires, then if/when you subsequently need to travel to the US, then your best option will be to apply for an ESTA on your UK passport. When you do this, you should answer “yes” to the question about having been denied a visa previously, as YOU have been, and that’s what matters (it’s not related to your citizenship/etc).
When you do this your ESTA may be approved or it may be rejected. If it’s approved, you’re good to go. If it’s not, then you will need to obtain another visa at that time.
Update: OP updated their question to note they already have a valid US visa! Then just use that and don’t apply for a new ESTA or visa. See I have two passports/nationalities. How do I use them when I travel? for how to travel with two passports.
Original answer assuming you don’t already have a visa:
You should answer yes. All the questions are about you, not your passport or nationality, so becoming a UK citizen does not change the fact that you were previously denied a visa.
Your best option is to apply for a B-2 visa. It’s an expensive hassle, but based on what you’ve told us it’s highly likely to get approved, and it’s much better than getting busted for lying on the ESTA application form.
Credit:stackoverflow.com‘
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