Richard was the son of Thomas Abberbury (or Adderbury), a younger son from a prominent Berkshire and Oxfordshire family. When he was fifteen, his father unexpectedly inherited the family estates, centred on Donnington in Berkshire and Steeple Aston in Oxfordshire, from Richard’s cousin, Sir John Abberbury, when he was killed at the Siege of Calais. So, when Thomas died in 1353, his son became an extremely wealthy man. Around the same time, he married Agnes, the daughter of Chief Justice Sir William Shareshull.

Richard’s career began as a military one, serving with Henry of Grosmont, Duke of Lancaster in Brittany and Normandy in 1356. However, after the Treaty of Bretigny, he soon transferred to the retinue of the Black Prince, his feudal overlord, who knighted him by 1359. In that year, he accompanied the Prince to Gascony and he fought alongside him throughout the Najera campaign seven years later. For his valiant service, he was given an annuity of £40 in return for his military support during times of war. He thus appeared at the Northampton muster of 1368 with four esquires and ten archers and served in Gascony the following year, remaining as Seneschal of Limousin upon Prince Edward's return to England in 1371. Subsequently, he was placed in charge of a force of 39 men-at-arms and 40 archers and was put to sea for five months in the Spring and Summer of 1374.

After the death of the Black Prince in 1376, Sir Richard continued to serve his widow, the Fair Maid of Kent, and her son, the future King Richard II. He became the boy’s 'master', responsible for his safety and upbringing, and was so concerned for his immediate welfare that, within a month, he had sold two of his own Sussex manors in order to prop-up the boy’s estate. He was only to be recompensed for this selfless act many years later. The prince’s accession to the throne seems to have little altered Abberbury’s position at court. In 1377, he negotiated a reconciliation between Prince John of Gaunt and the citizens of London and, presumably as a reward, he was granted life custody of Dartmoor Forest soon afterward. At the end of the same year, he was commissioned to make an inventory of the late Edward III’s jewels and other valuables, with powers to seize any found to be in the possession of others, notably from Alice Perrers, the King’s former mistress.

In 1378, Sir Richard became joint Captain of Brest Castle in Brittany, along with his neighbour, Sir John Golafre. They sailed from England with a company of 140 men in the 'Alice', a ship which the King had given to Abberbury, and remained at their post of almost a year. Sir Richard then returned to England briefly in the Summer before accompanying John de Montfort, the Duke of Brittany, back to his duchy to negotiate the terms of an Anglo-Breton alliance. Following this experience, Sir Richard now became a trusted Royal diplomat. He was sent to Bruges in 1380 to negotiate King Richard’s marriage to Anne of Bohemia with the representatives of her brother, Wenzel IV, King of the Romans. Sir Richard extended the trip by travelling to Germany for a personal audience with the King, staying abroad for some three months. After the marriage, Abberbury was a natural choice to become attached to the new Queen’s household and he was appointed chamberlain soon after her Coronation in 1382. He served her well for the next four years, and she rewarded him in 1383 with a life-grant of the manors of Iffley in Oxfordshire and Carswell, at Buckland, in Berkshire. These were later given to him outright by the King in compensation for Sir Richard having earlier sold his Sussex estates for his patron's upkeep when still a child. His trusted position in the King’s inner circle is further indicated by his acting as both a trustee for the estates of the King’s disgraced half-brother, Sir John Holland, and executor of the will of the King’s mother, the Fair Maid of Kent. In 1386, Sir Richard was even given permission to turn his manor at Donnington into a fortified castle.

It is not surprising, therefore, to find Sir Richard amongst those expelled from the King’s presence by the Lords Appellant when, concerned about the excessive influence of Royal favourites, they took control of the government in 1388. Fortunately, though Sir Richard could easily have been executed, he was not even imprisoned and, the following year, he was back at the King’s side when he re-established his control. Now a member of the King’s Council, King Richard made even wider use of his experience in matters of Foreign policy. In 1390, he was sent as ambassador to negotiate a permanent peace with the French, and then a truce with the Flemmings. Soon afterwards, he is found sending letters to the Pope, on the King’s behalf, confirming policies set out in the Statute of Provisors. Whilst, in council, he advised on breaches of the truce in Aquitaine. He also sat on the Queen’s council during this time, but she died of the plague in 1394. However, as her treasurer and receiver-general, he continued to audit her household accounts in the period after her death. He spent the following winter in Ireland with the King’s forces, but now began to reduce his workload, both locally in Berkshire and Oxfordshire and as a Royal councillor, from which he finally stepped down in 1396.

When Abberbury died in April 1399, he left substantial estates to his son and namesake. He had added to his key holdings by purchasing Peasemore in Berkshire in 1378, the Bailiwick of Wychwood and a life-interest in the Golafre lands at Langley in Oxfordshire in 1380, the reversion of the manor of Kidlington and a town-house in Distaff Lane in London. Although he had sold Carswell, and Iffley he had charitably given away. In 1366, Sir Richard had established a chantry chapel at Donnington which, eventually, he handed over to the Crutched Friars from near the Tower of London. It expanded to become a small dependant friary and, in 1393, he gave Iffley to the still-extant charitable hospital (or almshouses) which he built alongside, and with which his name will forever be associated.