cier, m.n: a turn, time, business, affair.
The “ci” sounds like “ch” in Old English, which brings us to the etymology of Charing Cross.
The “Cross” refers to the cross that King Edward I erected in memory of his wife, Eleanor of Castile, in 1291-1294. This wooden cross was destroyed in 1647 during the Civil War. A replacement cross was commissioned in 1865, but it is of an ornate Gothic design, unlike the original. Fragments of the original medieval cross remain in the Museum of London.
Now for “Charing”. The hamlet where the original cross used to stand was called Charing, which derives from Old English “cier”, a turn or bend. The hamlet was located at a bend in the River Thames.
Image from Tom Hall’s London and Overseas Travel blog. It’s the mural on the platform of Charing Cross Underground Station.