Trump backs a full campaignFriday, Trump publicly asked Graham to put her name on the ballot. “During her visit, I asked Darline, for the Good of our Nation, to run for the U.S. Senate,” Trump wrote on Truth Social. Over a week after the death of Sen. Lindsey Graham, Sen. Darline Graham tells @seanhannity she's running for the full Senate term to replace her brother in South Carolina. It needs President Trump’s strongest ally in the United States Senate,” Fry wrote Monday on X. Republicans have held the seat since 1998, making the GOP primary the race most likely to decide who succeeds Lindsey Graham for the next six years.