He was born in London on 4 November 1896, the second son of the 2nd Baron Alington of Crichel Down, Wimborne, Dorset,  and Lady Feodorowna Yorke.

He was educated at Eton and matriculated in 1915. In November 1918, his elder brother died of wounds and Napier succeeded to the title on the death of his father, the following July. He served as a Captain in the RAF during the war.

He dated Tallulah Bankhead in the 1920s. She met him when she was appearing in “Nice People” and they later resumed their affair when she moved to England.  He was said to be charming, reckless and bisexual. He proposed to Tallulah shortly after they met, but she was more interested in her career than marriage. He married Lady Mary Sibell Ashley-Cooper, daughter of the 9th Earl of Shaftesbury, on 27 November 1928. Their only child, Mary Anna Sibell Elizabeth Sturt was born in 1929. Lady Mary died in 1936.

On 2 July 1940, he was commissioned as an RAFVR officer in the Administrative and Special Duties Branch and was posted to Cairo, possibly serving as a staff officer at HQ Middle East.

He died on 16 September 1940 in Cairo of pneumonia. As he had no male heir, the title became extinct on his death. He is buried in the New British Protestant Cemetery in Cairo Plot E. Grave 221-222.

Because of the early deaths of her mother and father, his daughter had a lonely childhood. She joined the Brownies' pack at Buckingham Palace with Princess Margaret, and went to Miss Faunce's Parents' National Union School at Lancaster Gate, which moved after the outbreak of war to Wimborne St Giles, the home of her grandparents, the Earl and Countess of Shaftesbury. She then went to Cheltenham Ladies College. She married Commander Toby Marten, DSC.

She was the Dorset landowner whose battle to obtain the return of several hundred acres of farmland at Crichel Down, near Wimborne, became a cause célèbre which exposed the obdurate power of modern government after the Second World War.

The land was part of 725 acres purchased under pressure by the Air Ministry for a practice bombing range in 1938. Four years later, Winston Churchill, as prime minister, promised that it would be offered back to the owners. Inevitably the post-war Labour administration had scant sympathy for the rights of the landowner, but it came as a shock when the Churchill government's return to power in 1951 produced no change in official policy. This promise was not honoured. Instead, the land (then valued at £21,000) was handed over to the Ministry of Agriculture who vastly increased the cost of the land beyond the amount the original owners could afford (£32,000) and leased it out.

In 1949 the Martens, now the owners of the Crichel Estate, began a campaign for the Government promise to be kept, by a return sale of the land. They gained a Public Enquiry which was chaired by Sir Oliver Franks. His Report was damning about actions in the case taken by those acting for the Government.

The Minister responsible resigned, and the Crichel Estate part of the land was sold back to the Martens.

From "Whose land was it anyway? The Crichel Down Rules and the sale of public land" by Roger Gibbard:-
In the history of modern parliament, the Crichel Down affair takes on momentous significance, and has been described as a ‘political bombshell’. The public inquiry into the Crichel Down events revealed a catalogue of ineptitude and maladministration and resulted directly in the resignation of the Secretary of State for Agriculture (Sir Thomas Dugdale), then a senior cabinet position, and was the first case of Ministerial resignation since 1917. Whilst the underlying case was, in the scale of things, trivial, involving the transfer of some seven hundred acres of mediocre agricultural land in Dorset, the ramifications for subsequent government procedure have been enormous, and it is regarded as one of the key events leading to the creation of the post of Ombudsman. Crichel Down was probably the first instance of close and very public scrutiny being directed at a Minister of the Crown in the execution of his duties.

Mrs Marten died in 2010.