Who struck down Gedaliah, the governor appointed by the king of Babylon?

Answer: Ishmael son of Nethaniah

Ishmael son of Nethaniah and ten men killed Gedaliah son of Ahikam with the sword, though Johanan had warned Gedaliah.

“and said to him, “Are you aware that Baalis king of the Ammonites has sent Ishmael son of Nethaniah to take your life?” But Gedaliah son of Ahikam did not believe them.”— Jeremiah 40:14 (BSB)