Elias gained a law degree from Auckland University in 1970, and then undertook further study at Stanford University. She took up employment with an Auckland law firm in 1972, beginning her career as a barrister three years later. She also served as a member of the Motor Sports Licensing Appeal Authority and of the Working Party on the Environment. She served as a Law Commissioner from 1984 to 1988. Elias is also known for her work in relation to various Treaty-related cases. She was made a Queen's Counsel in 1988, and in 1990, she was awarded a commemorative medal in recognition of her services.
Elias became a judge of the High Court in 1995, and occasionally sat on the Court of Appeal. On 17 May 1999, she was sworn in as Chief Justice, the first woman to hold that position in New Zealand. When the government announced plans for the establishment of a Supreme Court (replacing the old links to the Judicial Committee of the Privy Council), it was decided that Elias, as Chief Justice, would automatically be appointed to the new body. The Supreme Court is scheduled to open in the middle of 2004.