He was born in Ashby-de-la-Zouch, Leicestershire, the eldest son of Francis Hastings, 2nd Earl of Huntingdon, and Catherine Pole. He was educated at first by private tutors at his family manor. A year or so senior to Edward VI, Hastings joined the young prince at his studies at the king's invitation. He was tutored under Richard Cox, John Cheke and Jean Belmain. They provided both youths with an education based in the principles of Humanism. In 1548 he spent a brief period at Queens' College, Cambridge, profoundly influenced by the evangelical Protestantism he encountered at court and at the university.
His father was a political ally of John Dudley, 1st Duke of Northumberland, and to further their alliance the two elder politicians arranged the marriage of their children. On 21 May 1553, Henry was wed to Katherine Dudley, daughter of Northumberland by Jane Guildford.
In 1553, Edward VI was dying and his appointed heir was his cousin Lady Jane Grey, Northumberland's daughter-in-law. Jane's reign lasted only from 10–19 July 1553 until her cousin Mary I of England prevailed. Due to his marital alliance, Henry backed Northumberland in his attempt to divert the succession in favour of Lady Jane Grey in July 1553, and on Mary Tudor's triumph he found himself incarcerated in the Tower of London. Mary attempted to reconcile with the Hastings family and soon they were free again and by oath loyal to her.
Henry entered the household of his great-uncle Cardinal Reginald Pole and followed him in his visits of Calais, Flanders and the monasteries of Smithfield, London. The two men also escorted the later Philip II of Spain from the Seventeen Provinces to the Kingdom of England for his marriage to Mary. Despite his personal loyalty to Mary and his great-uncle, Hastings practised Calvinism and showed little financial restraint in supporting his puritan beliefs. Among those notables who benefited from his family's friendship and patronage were John Brinsley the elder, Arthur Hildersham, Thomas Cartwright, Lawrence Humphrey, Thomas Sampson, Anthony Gilby, John King, and William Chaderton.
He had been loyal to Edward VI, Jane and Mary I during their respective reigns and his father remained an influential politician. When Mary I died childless and was succeeded by her younger half-sister Elizabeth I in 1558, the new queen also counted on the reliable Hastings family among her supporters. Together with the second earl, Lord Hastings received a summons to the Lords in the first parliament of Elizabeth, and attended assiduously, being present (among much else) at the passage of the Acts of Supremacy and Uniformity in the spring of 1559. Henry was named a Knight of the Bath by the new queen regnant.
His father died on 25 January 1560 and Henry became the third Earl of Huntingdon. He thus assumed responsibility for his widowed mother and his ten brothers and sisters.
With his humanist education, experience of court life, and a brother-in-law, Robert Dudley, high in the new queen's favour, Huntingdon might well have expected early advancement. However, at the time few members of the Tudor dynasty remained alive and several descendants of the previous English royal house of Plantagenet were seen as possible heirs to the throne. Huntingdon was among these possible heirs and won a certain amount of support, especially from the Protestants and the enemies of another claimant Mary, Queen of Scots. Huntingdon soon discovered that his Yorkist ancestry barred his way. Indeed, when Elizabeth fell ill with the smallpox in October 1562, the Protestant group put him forward as a potential successor and, though he subsequently did all in his power to convince her of his loyalty, the queen proved very slow thereafter to employ him outside his native county of Leicestershire.
However, he was still useful to her. It was doubtless felt that the earl's own title to the crown was a pledge that he would show scant sympathy with the advocates of Mary's claim. For three months during the northern uprising in the autumn of 1569, he assisted George Talbot, 6th Earl of Shrewsbury to remove the Scottish queen from Wingfield Manor to Tutbury. He was later one of the Peers at her trial in 1586. Elizabeth formally recognized his service by creating him a Knight of the Garter in April 1570 alongside William Somerset, 3rd Earl of Worcester, and from this time seems to have regarded him as a candidate for promotion. The rebellion of the earls had demonstrated the ineffectiveness of Thomas Radcliffe, 3rd Earl of Sussex as president of the council in the north, in 1572 Huntingdon was appointed president of the Council of the North. Throughout the period the north of England stood as a buffer zone against Scotland, still in a highly volatile state after Mary's flight.
He was prominent and active in the preparations of 1588 for the Spanish invasion.
Having gone north to Newcastle to oversee the musters in the autumn of 1595, Huntingdon planned to join his wife at court for Christmas. On his return to York in late November, however, he fell ill with a fever and died there on 14 December 1595. At court Elizabeth went out of her way to comfort his distraught widow, though she did little to mitigate the debts. Childless, Huntingdon had educated Francis Hastings, the eldest son of his brother, Sir George Hastings, as his heir, sending him for a time to Geneva. Francis's ten-year-old son Henry was being brought up in his great-uncle's household at York in 1595. Since his brother had died intestate, George, fourth earl of Huntingdon, tried to avoid taking up the administration of his estate, but the queen insisted upon Huntingdon's being given a funeral commensurate with his rank, and he was buried with his nephew, Francis, who only outlived him by three days, at St Helen's Church, Ashby-de-la-Zouch, on 26 April 1596. A portrait of Huntingdon in armour dated 1588 now hangs in the Tower.
His great-grandfather was Lord William Hastings esteemed friend and ally of Edward IV and who was beheaded in 1483 at the direction of Richard III. His paternal grandparents were George Hastings, 1st Earl of Huntingdon, and Anne Stafford, Countess of Huntingdon. His maternal grandparents were Henry Pole, 1st Baron Montagu, and Jane Neville, a daughter of George Nevill, 4th Baron Bergavenny, and his wife Margaret, daughter of Hugh Fenn.
Anne Stafford was a daughter of Henry Stafford, 2nd Duke of Buckingham, and Catherine Woodville. Henry Pole was a son of Sir Richard Pole and Margaret Pole, 8th Countess of Salisbury. Margaret was the only daughter of George Plantagenet, 1st Duke of Clarence, and Isabella Neville, Duchess of Clarence. Both Buckingham and Clarence were descendants of the House of Plantagenet, were close relatives to various monarchs of England and entertained hopes for the throne during their lifetimes.
Huntingdon was responsible for the compilation of an elaborate history of the Hastings family, a manuscript copy of which is now in the British Museum.