Molesworth was commissioned into the Somerset Light Infantry as a second lieutenant in March 1910. After this time he served in Malta, North China and India. He served during the First World War in India with his battalion, and served as Adjutant of the 2nd battalion from 1916 to 1919. He saw action during the Third Anglo-Afghan War, where he was Mentioned in Despatches. He also served as Deputy Assistant Adjutant General at Army Headquarters India during 1919 and 1921 and in 1924, and was made Brigade Major in 1925. Between the years 1926 and 1927 he served as Deputy Assistant Quartermaster General at Army Headquarters India.