MOSCOW — Ukraine’s president, Volodymyr Zelensky, fired his chief of staff on Tuesday in a personnel shake-up affecting central figures on the Ukrainian side of the events leading to the impeachment trial of President Trump.

The shuffle in Kyiv, the Ukrainian capital, offered fresh evidence of how deeply entangled Ukrainian and American politics have become.

The new chief of staff, Andriy Yermak, negotiated last summer with President Trump’s personal lawyer, Rudolph W. Giuliani, as Mr. Giuliani and American diplomats pressured Ukraine to start investigations that would benefit Mr. Trump politically. Mr. Yermak, who at the time was a senior presidential adviser on foreign policy, has sought to maintain good ties with the Trump administration.

The man he replaced, Andriy Bohdan, a former lawyer for the oligarch Ihor Kolomoisky, reportedly became chief of staff last year over Mr. Giuliani’s objections. Mr. Giuliani was at odds with Mr. Kolomoisky at the time, but later pivoted to working with Kolomoisky associates in his search for evidence against Mr. Trump’s political enemies.