George Kirwan started his teaching career at Wick Private School, Brighton, in 1883. In 1886, he moved to Coatham Grammar School, in Redcar, and then to Wiggeston School, Leicester from 1888 to 1895.

In 1896, when Dakyns left the High School to go to Morpeth, Kirwan was appointed to replace him as Headmaster. His main subjects were mathematics and languages and, as the Shields Gazette described him, he was "an examplary head teacher".

Kirwan had to steer the school through difficult financial times. First of all, a bankruptcy when it had failed to attract enough pupils, and then the company which owned the school gave it up and sold it to the local authority.

In 1919. Kirwan took ill. He requested a leave of absence in order to undertake a course of treatment but, sadly, he died a month before he was scheduled to take it. At his funeral, some sixty High School Cadets led the hearse, followed by a large number of boys from the school.

In 1935 his son, Geoffrey Dugdale Kirwan, donated £100 to establish prizes in his father's memory. For many years afterwards, the Kirwan Prize was awarded for Latin, French and General Knowledge.