Neil James Archibald Primrose (14 December 1882 – 15 November 1917) was a British Liberal politician and soldier. The second son of Prime Minister Lord Rosebery, he represented Wisbech in parliament from 1910 to 1917 and served as Under-Secretary of State for Foreign Affairs in 1915 and as joint-Parliamentary Secretary to the Treasury from 1916 to 1917. He died from wounds received in action in Palestine in 1917.

Primrose was born at Dalmeny House near Edinburgh, the second son of Archibald Primrose, 5th Earl of Rosebery, Prime Minister to Queen Victoria from 1894 to 1895, and Hannah de Rothschild, daughter of Baron Mayer de Rothschild. He was the brother of Harry Primrose, 6th Earl of Rosebery and writer Lady Sybil Grant.

He was educated at Eton and Oxford and played No.1 for the Oxford Polo team in 1904 and 1905. While at Oxford he was also a keen steeplechase rider.

Primrose entered the House of Commons at the January 1910 general election as Member of Parliament (MP) for Wisbech. In 1913 he became a member of the Anglo-American Peace Centenary Committee. In February 1915 he was appointed Under-Secretary of State for Foreign Affairs in H. H. Asquith's Liberal administration, but was not offered a post when the coalition government was formed in May of the same year. When David Lloyd George became prime minister in December 1916, Primrose returned to the government as joint-Parliamentary Secretary to the Treasury (government chief whip) alongside Conservative Edmund FitzAlan-Howard, a post he only held until March of the following year. In June 1917 he was sworn of the Privy Council.

Primrose was commissioned into the Buckinghamshire Yeomanry (Royal Bucks Hussars) in 1909. Promoted Captain in 1915, he was awarded the Military Cross in the King's Birthday Honours of June 1916. He died in November 1917 from wounds received in action at Gezer during the Sinai and Palestine Campaign while leading his squadron of the 1/1st Royal Buckinghamshire Yeomanry against Turkish positions on the Abu Shusheh ridge during the Third Battle of Gaza.

When news of the death of Primrose reached the UK, Prime Minister David Lloyd George paid tribute in the House of Commons on 19 November 1917, alongside his report of the death of Lieutenant General Sir Stanley Maude:

May I be permitted before I sit down to utter one word of another who held an inconspicuous position in the Army but who was well known to all Members of this House. I refer to Captain Neil Primrose. The House knew his bright and radiant spirit well. To his intimates he was one of the most lovable men we ever met. He had ability far above the average, and, in spite of the reserve and shyness which held him back, his future was full of hope. He had already rendered distinguished service in the field, and for that service he had been recognised at the suggestion of his commanding officer; and he might well, for he had many offers, have occupied positions where he could have rendered services to the public, positions honourable to him, but positions of personal safety, and the fact that he had been chosen by his constituents to serve in this House would have rendered his acceptance of these positions honourable to himself. He chose deliberately the path of danger. He fell charging at the head of his troops, at the very moment of victory, and Members of the House will, I feel certain, join me in an expression of deepest sympathy with those whom he has left behind to mourn him.

— David Lloyd George, House of Commons parliamentary debate, 19 November 1917