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)

Around mid-2000s, Dan Lewis and his fiancée were engaged to be married. But two days before the wedding, his fiancée changed her mind. She informed him that she "couldn't bear spending the rest of her life with [him]" and "thought she could do better". (TV: Once, Upon Time)

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)