Haverty played for Home Farm and St Patrick's Athletic before signing for Arsenal in July 1954.

[4][5] Haverty also played in the London XI that contested the inaugural edition of the Inter-Cities Fairs Cup.

[5] Back trouble meant he missed some of Arsenal's matches during this time,[2] but put in 37 appearances and 8 goals in 1959–60,[4] his best season for the club.

Haverty was unhappy with the lack of a regular first-team place, and put in a transfer request; he was sold to Blackburn Rovers in August 1961 for £25,000.

[1][5] He moved back to his native Ireland to play for Shelbourne, with whom he won the last of his 32 full international caps.