Quarles made a single first-class appearance for Norfolk against the Marylebone Cricket Club (MCC) at Lord's in 1820.
[1] The MCC scored 473 all out in their first-innings, in response Norfolk managed just 92, with Quarles batting at number eleven and ending unbeaten on 0.
[2] A decade later he appeared in his second first-class match, this time for Suffolk against the MCC at Field Lane, Bury St Edmunds.
[1] The MCC made 100 all out in their first-innings, with Suffolk making 74 in response, with Quarles being dismissed for a duck by Herbert Jenner.
However, Suffolk well just short in being bowled out for 82, with Quarles contributing 4 to the total before he was dismissed by Ned Wenman.