Complex sentence: The captain of "Unicorn" was killed, and Clements, after conducting the fight to a successful issue, brought the prize into Kinsale and went out again in pursuit of the privateer's consort, which was also captured and brought in.
Split into simpler sentences: The captain of "Unicorn" was killed, but Clement assumed command and secured the capture of the privateer. The French vessel was brought into Kinsale; and Clement immediately took "Unicorn" back to sea in pursuit of a second French vessel, which was also captured and brought in.