Hely was the son of Frederick Augustus Hely, an Irish public servant who was appointed as the Superintendent of Convicts in 1823. He was educated at The King's School, Parramatta and was initially employed as a clerk in the Colonial Secretary's office. He took part in the 1846-47 expedition of Ludwig Leichhardt but was accused by Leichhardt of indolence, disloyalty and "disgusting" behaviour. Nonetheless, he was put in charge of the official expedition to find Leichhardt in 1852. After 1841 Hely managed his deceased father's estates in the Brisbane Water district including Wyoming Cottage. He inherited a fifth share of the estate when he turned 21 and borrowed heavily against it, to finance a trip to England in 1858. As a result of these debts, Hely was bankrupted in 1865.