She spent most of her career working at the University of Auckland, where she rose to be Dean of its Faculty of Law. From 2006 to 2010, she was Registrar of the University of Oxford; the Registrar is the head of the university's administration and is one of its most senior figures.
Maxton was born on 31 August 1955 in Scotland. While at school, she played sport at international level, representing Scotland in lacrosse and hockey.
She studied at law at University College London, and graduated with a Bachelor of Laws (LLB) degree in 1976. She then trained as a barrister, and was called to the bar at Middle Temple on 27 July 1978.
Maxton moved to New Zealand after qualifying as a barrister. She undertook postgraduate study in law at the University of Canterbury, and graduated with a Master of Laws (LLM) degree in 1981.
At the University of Auckland, she also undertook postgraduate research and completed her Doctor of Philosophy (PhD) degree in 1991. Her doctoral thesis is entitled Contempt of Court.
Maxton began her academic career at the University of Canterbury. There, she taught within the university's School of Law as a lecturer. Upon marrying, she moved to a different university, the University of Auckland. This was unusual in that it is uncommon for academics to move between New Zealand law schools.
At the University of Auckland, New Zealand, Maxton's career was both academic and administrative. Joining the university in 1985 as a lecturer, she was promoted to senior lecturer in 1987 and later to associate professor. She spent periods as the Dean of Graduate Studies and was twice the acting Deputy Vice-Chancellor.
In 1993, she was appointed a Professor of Law. She was Dean of the Faculty of Law between 2000 and 2005.
During her academic career, Maxton was also a practising barrister. She concentrated on appellate cases. On 18 October 2012, she was made a Master of the Bench of Middle Temple.
From 2006 to 2011, Maxton held the position of Registrar of the University of Oxford. In that role, she head of the University of Oxford's administration. She was the first woman to hold the office in the 550 years since the position was first established. During the appointment, she was also a Fellow of University College, Oxford. She was succeeded by Ewan McKendrick in January 2011.
In 2011, Maxton was appointed Executive Director of the Royal Society. The Royal Society is possibly the oldest learned society still in existence and serves as the United Kingdom's academy of sciences. She is the first woman to be appointed to the position in its 350-year history.
She was married to Major Jim Carson, the first leader of the New Zealand Army Band and later Head of Music at Auckland Grammar School. Together, they had one son; James. Jim predeceased his wife, having died in 2008 of cancer.
In 2014, Maxton was awarded the Distinguished Alumni Award by her alma mater, the University of Auckland.
She was appointed Commander of the Order of the British Empire (CBE) in the 2017 Birthday Honours for services to science, law, and education.