His business was carried on by his son George Newenham (c.1750–1821), businessman and patron of the arts. He was operating on the North Mall, Cork city, by 1764, as a newspaper report in that year mentions that 18 guineas (£18.90) in gold and silver was stolen from his worsted shop. From 1770 he sold large quantities of worsted to George Gurney of Norwich. The Gurneys were among the most important clothing manufacturers in East Anglia. Prior to 1770 the main supplier of worsted was John Pim, a Dublin-based quaker, but a dispute over prices meant that Pim preferred to supply a rival company in Norwich. Newenham also had heated arguments with Gurney and on occasions threatened to sell his stock to a competitor. But in the early 1770s Newenham was able to benefit from a temporary shortage in woollen stuffs and sold at relatively high prices. Little is known about his merchant career in the 1780s and ‘90s. His last recorded business enterprise was in 1799/1800, when he established a bank – known as Newenham's Bank – in Cork city, along with his son George junior and John Lecky (qv). From the start it would appear that Newenham was a silent partner and that Lecky took care of the day-to-day running of the business. By 1809 the bank was situated on Patrick St. in a building valued at £85. Though it was one of the relatively small private banks in the south of Ireland, its finances were robust enough to survive the banking crisis of 1820.
Much of George Newenham's time and energy was taken up pursuing artistic and scientific interests. In 1774 George Gurney wrote to his son: ‘George Newenham is a very clever young fellow and if tho [sic] hast a mind to divert thyself with contemplating the starry regions, he will be an agreeable companion for thee, as he has made astronomy his great study’ (Friends Hist. Soc. Jn., xx, 77). Newenham reputedly built a telescope to his own design so that he could view the stars from his country seat. By 1800 his address was Summerhill, a country house near Cork city. This became an important focal point for artistic activity in Cork. As a child Daniel McAleese (qv) was a frequent visitor and was quite taken with the large picture gallery, with many works by the Irish painters Nathaniel Grogan (qv) and John Butts. Newenham took the young Maclise under his wing and even gave him a job in his bank, which he endured for just a year. The sculptor John Hogan (qv) was another to benefit from Newenham's generosity. In 1816 Newenham lent part of his collection to an exhibition organised by the Cork Society of Arts. He had an unusually hands-on approach to patronage and would give artists working space within his own home. Maclise's biographer mentions that ‘colours, canvas and the easel, the model stand and clay were familiar objects’ at Newenham's home (O'Driscoll, Memoir, 18–20). Newenham died 21 October 1821, apparently as a result of catching a cold while clay modelling. His bank was wound up that year but reestablished for a few months by George Newenham junior in 1824; the bank closed for good in 1825 and creditors were paid in full.