Okyoku Reijo to Shuka no Kisetsu: Reitetsu Saishou-sama to no Jimu-teki na Konin Keiyaku ni, Fuman wa Gozaimasen

お局令嬢と朱夏の季節~冷徹宰相様との事務的な婚姻契約に、不満はございません~

Adaptation

The Noble Spinster and the Season of Red Summer
Okyoku Reijou to Shiyuka no Kisetsu: Reitetsu Saishou-sama no Okazari no Tsuma ni Natta Hazu ga, Dekiaisareteimasu· お局令嬢と朱夏の季節 〜冷徹宰相様のお飾りの妻になったはずが、溺愛されています〜
manga

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)