Having fought at The Battle of Jutland during the First World War, Chiswick, London born inside forward Harry Anstiss began his football career with Hammersmith Athletic in 1919. In August 1920 he joined newly elected Football League club Brentford as an amateur, making his debut at Norwich City that October and turning professional the following month, and during 1921-22 he second top scored for The Bees with 15 goals in only 25 appearances, including a hat-trick against Brighton & Hove Albion in April 1922. His performances led to his transfer to Millwall for £650 in May 1922 after 19 goals in 44 games for The Bees.
However after 3 goals in 19 appearances for The Lions, he was moved on to Watford for £150 in June 1923, where again he only stayed a single season, scoring three times in 18 matches for The Hornets. A free transfer to Rochdale followed in June 1924 and it was at Spotland that Anstiss ignited his career, being ever present in 1924-25 and top scoring with 23 goals as Rochdale finished 6th in the Third Division (North). A further impressive season with Anstiss scoring 16 goals in 30 appearances as ‘Dale finished third saw a £1,000 transfer to First Division Sheffield Wednesday in July 1926, although he struggled to get into the first eleven scoring 5 times in 12 appearances during 1926-27 before joining Port Vale in February 1927, along with ‘a substantial financial consideration’ in exchange for Alf Strange.
He had a great start to his Vale career, scoring on his debut in a 6-2 win over Notts County at The Old Recreation Ground on 26th February. He went on to score a hat-trick in a 7-1 home win over Fulham on 2nd April, and claimed 11 goals in 15 Second Division games in the 1926-27 campaign. This proved the end of his purple patch, as he scored five goals in 32 games in the 1927-28 season. Injury brought him down in November 1928, and limited him to three goals in 17 matches in the 1928-29 relegation season. However he scored 15 goals in 37 appearances in the 1929-30 season, as The Valiants were crowned Champions of the Third Division (North). He fell out of favour in October 1930, and was limited to six goals in 17 games in 1930-31 and he was then transferred to Swansea Town in May 1931 after 40 goals in 117 appearances.
His two years at The Vetch Field yielded 6 goals in 29 appearances before he transferred to Crewe Alexandra in July 1933, where he scored 7 times in 31 appearances before a move to Gillingham in July 1934. His single season at Priestfield, where he scored 6 times in 34 appearances for The Gills, proved his last in League football, and he joined non league Tunbridge Wells Rangers in the summer of 1935 and subsequently Cray Wanderers in 1936 before retiring in 1937.