Otsubone Reijou to Shuka no Kisetsu: Reitetsu Saishou-sama no Okazari no Tsuma ni Natta Hazu ga, Dekiai sareteimasu

Having had her engagement broken off and now past the age of marriage, Alerila is known behind her back as the "official lady." She works steadily as the right-hand man to the "cold-hearted Prime Minister," Marquis Easteria Wegmund. One day, while on duty, the Prime Minister proposes to her. Given rumors that the Prime Minister is in love with another woman, Alerila's own low family status, and her status as an unmarried administrative officer, she understands that he is asking her to enter into a contract marriage, and so she accepts the engagement. A businesslike married life with the cold-hearted Prime Minister begins...!!

(Source: Comic Earth Star, translated)