Based in Garryduff, Gowran, County Kilkenny he first gained success in the 1986 Tipperary Cup.
In 1999 he reached the final of the 1999 Irish Greyhound Derby for the first time with Mr Bozz.
[4][5] Hennessy remains one of Ireland's leading trainers and won the 2016 English Greyhound Derby with Jaytee Jet to complete the trio of national Derby race wins.
[7] Hennessy is also a horse trainer, training a small number of racehorses that compete in National Hunt racing.
He gained his biggest success to date when Heaven Help Us won the Coral Cup at the 2021 Cheltenham Festival.