WASHINGTON—A unit of NatWest Group on Tuesday agreed to pay about $35 million and pleaded guilty to wire and securities fraud in relation to a long-running scheme by some of its traders to manipulate U.S. Treasury debt markets. The lender’s investment bank NatWest Markets admitted its traders engaged in schemes to manipulate U.S. Treasury markets over a decade up to 2018. The firm agreed to serve three years of probation in addition to the fine and restitution, the U.S. Department of Justice said in a statement. The fine is another setback for the British state-backed bank’s efforts to clean up its image under Chief Executive Alison Rose, including a rebrand of the group from the scandal-tainted Royal Bank of Scotland name last year. The bank is still majority-owned by British taxpayers after its bailout in the 2008 financial crisis. Tuesday’s plea agreement comes little more than a week after NatWest …