Born into a family of Durham dyers, Trollope began his long military career in France in the 1420s as a man-at-arms, serving first on Tombelaine under Thomas Burgh and then with the garrisons at Fresnay-le-Vicomte and Caen under Sir John Fastolf in the Duke of Somerset's raid into Picardy in February 1440. Trollope served in Matthew Gough's company. By 1442 he was lieutenant at Fresnay under Sir Richard Woodville and held the same position under Osbert Mundeford when he surrendered the castle to the French in 1450.
Some time before 1455 he married Elizabeth, sister of Osbert Mundeford (a protégé of the Beaufort family, who became treasurer-general of the duchy of Normandy in September 1448), and this connection allowed Trollope to prosper in his military career. By 1455 Trollope was made Master Porter of Calais, a capacity in which he continued to serve until 1459. It was in this office that he prevented pirates and French ships alike from sailing, but also seized and stole from "the ships of allies and subjects alike" to such an extent that he has been called a "freebooter".
Shortly before the confrontation at Ludford Bridge, Trollope sailed for England with Richard Neville, 16th Earl of Warwick known as ("The Kingmaker"). At the Battle of Ludford Bridge Trollope commanded part of the Yorkist army of Richard of York, 3rd Duke of York, but betrayed him to the Lancastrians, bringing with him "valuable intelligence" regarding York's army.
Trollope returned to France with Henry Beaufort, 3rd Duke of Somerset to aid in the capture of Calais. Somerset failed to achieve this, but Trollope did persuade the garrison of Guînes to come over to the Lancastrians, and was appointed bailiff of Guînes on 24 March and expected to defend it. However, Somerset's defeat at the battle of Newenham Bridge (Pont de Nieulay) on 23 April and the failure of Mundeford to supply a relief force (it was intercepted at the port of Sandwich in June) forced Trollope to surrender Guînes to the Yorkists shortly afterwards, and he then returned to England.
Trollope proved to be an invaluable strategist to Margaret of Anjou. He took part in the ambush at Worksop on York's march north in December 1460 and then supposedly concocted the Lancastrian plan at the Battle of Wakefield, where York and Richard Neville, 5th Earl of Salisbury were killed. Andrew Trollope also fought at the Second Battle of St Albans (where he stepped on a caltrop) and was knighted by Prince Edward. His importance to the Lancastrian cause can be seen by the fact that, in March 1461, the recently proclaimed King Edward IV offered a £100 reward to anyone who killed "certain named enemies of the House of York", which included Trollope.
At the Battle of Towton (29 March 1461) Trollope shared the command of the Lancastrian vanguard with the Earl of Northumberland, against the Yorkist army of Edward IV. Considered the "opposite number" of his contemporary William Neville, 1st Earl of Kent, Trollope's death in the battle was "a damaging blow" for the future of the Lancastrian cause. He was posthumously attainted, and his son Sir David Trollope was also killed at Towton.
Trollop and his wife, Elizabeth Mundeford, had a daughter Margaret who married Richard Calle of Bacton, bailiff of the Pastons.