Andrew Thynne was born in 1847 at Ennistymon, Clare, Ireland. He arrived in Queensland with his parents in 1864 and joined the public service as a clerk. His career was short-lived and he went on to being admitted as a solicitor in 1873.
He was described a “brainy and industrious lawyer”, and he formed a partnership with Sir Edward Macartney, representing some of Queensland's largest corporations.
In January 1882, Thynne was appointed to the Legislative Council He reamined a Member until its abolition in 1922. He was the only Councillor in Cabinet in 1888-90 when he served as Minister of Justice in the McIlwraith and Morehead governments. In subsequent Cabinets he was Minister without portfolio (1893-94), Postmaster-General (1894-97) and Secretary for Agriculture (1896-98); he helped to establish the Queensland Agricultural College at Gatton.
Thynne represented his colony at the National Australasian Convention in Sydney in 1891, at a colonial conference held in Ottawa, Canada, in 1894 and at a postal conference in Hobart in 1895. In March 1898, he resigned his portfolio in order to give more time to his other professional interests.
As leader of the government in the Legislative Council and principal of the firm handling the Chillagoe Pty Co.'s legal interests, Thynne argued successfully for government assistance to his corporate client. In late 1916 he clashed acrimoniously with Premier T. J. Ryan over the attempted transformation of the company into a State-owned mining enterprise. He accused Ryan of forcing his clients to sell '”at a wrecker's price”. The Bill associated with the sale was defeated in the Council.
Thynne was appointed to the first Senate of the University of Queensland in April 1910, then elected Vice-Chancellor in 1916 and Chancellor in 1925. A traditionalist to the core, he argued successfully against fellow Senate member A. H. Barlow who advocated that criteria other than matriculation be used for university entry. As vice-chancellor, Thynne reaffirmed the position of the original Senate that university professors should not be involved in politics.
As a speaker, his debating skill, command of language, personal charm and persuasiveness compensated for his soft voice and his tendency to touchiness.
With his friend Archbishop (Sir) James Duhig by his bedside, Thynne died on 27 February 1927 at Thoonbah, his home in Highgate Hill. Duhig praised him as “an ideal adviser in the many weighty matters of State and private interest with which he was called to deal”.