In 1834, he was commissioned as an ensign in the 19th Regiment of Foot and promoted to lieutenant in 1837. At the request of Leopold I of Belgium, Seymour accompanied Prince Albert of Saxe-Coburg and Gotha on the latter"s visit to Italy in the winter of 1838–1839. Upon Albert"s marriage to Queen Victoria in 1840, Seymour became his Groom-in-Waiting, an office he continued as such after Albert"s death in 1861, to Victoria until 1876, when he became an Extra Groom-in-Waiting.
In 1840, Seymour was promoted to captain and exchanged to the Scots Fusilier Guards in 1842.
In 1854, he served with the Guards in the Crimean War and was present at the battles of Alma, Balaclava and Inkerman. He was wounded at Inkerman and also later at the Siege of Sevastopol.
In 1854, he was brevetted colonel and appointed a Companion of the Order of the Bath in 1857, having also received the Légion d"honneur (fourth class) and the Medjidie (fourth class). Promoted to major in 1858, lieutenant-colonel in 1863 and major-general in 1864, Seymour was made a baronet in 1869 and went on to command the troops in Malta from 1872 to 1874.
He was promoted to lieutenant-general in 1873, colonel of the 11th (North Devonshire) Regiment of Foot in 1874, Knight Commander of the Order of the Bath in 1875 and general in 1877.
Seymour died at Kensington Palace in 1890 and his baronetcy was inherited by his two-year-old son.