Harte's twin brother, David, and his sister, Emer, are also Ireland field hockey internationals.

The Harte brothers have lined out together with eight different field hockey teams – Bandon Grammar School, Cork Harlequins, Pembroke Wanderers, DCU, SCHC, Dabang Mumbai, Munster and Ireland.

[1][3][4][9][10][13] While studying for their Leaving Cert at Bandon Grammar School, Conor and David, also played for Cork Harlequins, helping them win the 2006 Irish Senior Cup.

[15] In 2008–09, together with his brother David, Ronan Gormley, Stuart Loughrey, Justin Sheriff, Craig Fulton and Alan Sothern, Harte was a member of the Pembroke Wanderers team that won the Irish Senior Cup,[16][17] the Men's Irish Hockey League[18] and the EuroHockey Club Trophy.

[25] Since 2014 Harte has played for Racing Club de Bruxelles in the Men's Belgian Hockey League.

[28] Harte played for Dabang Mumbai in the 2015 Hockey India League season, once again teaming up with his brother David.

[33] Harte made his senior debut for Ireland in August 2006 in a Celtic Cup game against France.

[23][24][34][35][42] Harte was also a member of the Ireland team that won the bronze medal at the 2015 Men's EuroHockey Nations Championship.