As chairman of the House Select Committee on Benghazi, Mr. Gowdy led a two-year investigation into the 2012 attack in Libya that was sharply criticized by Democrats as a vehicle for Republicans to investigate Hillary Clinton, who was secretary of state at the time and went on to become the 2016 Democratic presidential nominee. Among the members of the committee was Secretary of State Mike Pompeo, then a Republican congressman from Kansas.

Mr. Gowdy was particularly critical of the State Department for not complying with requests for documents, and those past comments about the importance of responding to document requests are likely to resurface in any defense of Mr. Trump.

Mr. Trump’s legal team is not expected to expand substantially. Another of his personal lawyers, Rudolph W. Giuliani, is himself at the center of a controversy over Mr. Trump’s phone call with the Ukrainian president asking for an investigation into Hunter Biden, the younger son of one of his leading 2020 Democratic rivals, former Vice President Joseph R. Biden Jr.

In addition to Mr. Sekulow, the president had relied heavily on a small group of lawyers with experience as federal prosecutors to deal with the investigation led by the special counsel, Robert S. Mueller III, into Russian election interference.

But the impeachment inquiry, announced last month by House Democrats, might require a lawyer who can aid with a Senate trial.