Hypothetically, this is not an unusual query, and would have the usual answers.
Realistically, this may be a complicated situation, if it’s assumed that the person (dual UKC/USC) is accepting a position with the UK (National) government, and intends to retire in the UK on a civil service pension.
Your answer possibly lies in the US/UK Treaty, Article 19, paragraph 2, but dual citizenship may not make interpretation easy. I’m afraid you’re not going to appreciate my nonprofessional advice, but this needs to be answered by either one of two possibilities. Your first is the IRS who are usually reluctant to give opinions on queries involving a treaty (over the phone, for example). Your likeliest response would come from posing the question to them in writing, asking for their opinion. Your second option is a professional US/UK Tax Advisor.
I also trust that you’ve clarified, hypothetically, if there is any impact on US citizenship in accepting this particular UK (National?) government position. I assume you have, and that there are no problems.
Without the two above options, we can hope that someone who has been through this can respond, but given the complexity of the situation, I would want to be very certain of the expertise of the responder. I sincerely hope the situation is much simpler than I see it.
If in fact you were to be taxed by the US upon receipt of the pension, and since this would possibly be a nonqualified pension plan (no taxable amount shown on a Form 1099-R, a form you wouldn’t receive), you might want to read IRS Publication 939, The General Rule, for the deduction of contributions on taxable pension payments from nonqualified plans.