Engagement

Engagement, or being engaged, was the commitment to being married. If you were engaged, you were either a fiancé (male) or fiancée (female). Engagement rings were often worn. (TV: Cold Blood)

Weddings were preceded by a marriage proposal, (TV: Nightmare in Silver) then engagement. (TV: Black Orchid)

On Earth
The First Doctor accidentally became engaged to Cameca when he drank cocoa with her. (TV: The Aztecs)

By February 1945, Henry Barns was dating Jemima Fleming, and he didn't join the war effort due to an accident with a tractor. They became engaged shortly after World War II ended. (PROSE: In His Kiss)

Amy Pond and Rory Williams were engaged to be married on 26th of June, 2010. (TV: The Eleventh Hour)

In 2020, while searching the Doctor's pockets for a red pen, Amy found her engagement ring from Rory. (TV: Cold Blood)

Jake and Fay once became engaged. (PROSE: The Dead Man's Story)

In other societies
After marriage, and even engagement without marriage, female Ogrons became legal property of their male partners. (AUDIO: Too Many Masters)