Hossack was born in Walsall, but was educated at Chigwell School, playing for the school’s football team between 1882 and 1886, becoming team captain in his last year. He went up to Jesus College, Cambridge, collecting a "Blue" for Cambridge University in 1890.
After leaving university he joined the Corinthians club, from where he was selected for his first England appearance, against Wales on 5 March 1892. In this game, the selectors selected a team consisting mainly of players with Corinthians connections and awarded eight new caps. England were a little too skilful for the Welsh and ran out 2–0 winners with goals from Arthur Henfrey and Rupert Sandilands.
His second, and final, cap came two years later, also against Wales on 12 March 1894. Once again, the selectors decided to field a team consisting entirely of players with Corinthians connections. Wales opened the scoring after 10 minutes, but by half-time England had taken the lead with a goal from John Veitch and an own goal. Veitch scored again early in the second half and completed his hat-trick in the 80th minute, thus joining a select band to score a hat-trick on his début. The fifth goal came from Robert Cunliffe Gosling as England ran out comfortable 5–1 victors.
- "Hossack, Anthony Henry (HSK886AH)". A Cambridge Alumni Database. University of Cambridge.
- Graham Betts (2006). England: Player by player. Green Umbrella Publishing. p. 133. ISBN 1-905009-63-1.
- Gibbons, Philip (2001). Association Football in Victorian England - A History of the Game from 1863 to 1900. Upfront Publishing. p. 189. ISBN 1-84426-035-6.
- Gibbons. p. 259.