Dundee born to a Danish father, right back Harry Erentz began his football career with hometown club Dundee in 1895. At the end of the 1895-96 season, Erentz transferred to Lancashire League Oldham County, before signing for Newton Heath (Manchester United as is today) a year later, joining his elder brother Fred who went on to play some 300 times for Newton Heath through to 1902. It would be eight months, however, before Erentz made his debut for The Heathens, playing alongside his brother at right back in a 5-1 away defeat to Woolwich Arsenal on 8th January 1898. Erentz only made nine appearances for Newton Heath (six in the League and three in the FA Cup) between January and April before being transferred to Southern League Tottenham Hotspur in May 1898.
Erentz remained with Tottenham for six years, making appearances in 130 Southern League games and playing over 250 games overall, including most notably winning the 1901 FA Cup Final in a replay against Sheffield United at Burnden Park, Bolton after a 2-2 draw in the first match at The Crystal Palace, so helping Spurs to become the first and to date only club from outside The Football League to win the FA Cup. In December 1904, Erentz was transferred to Swindon Town, for whom he made 16 appearances before retiring through injury. He later became the trainer for London based amateur club The Corinthians.