Elvira Kovacs was born on 18 July 1982 in Zrenjanin, where she finished grammar school. She studied at the Faculty of Economics in Subotica, where she was also the student vice-dean, and studied for one semester at the Wirtschaftsuniversitaet in Vienna. She graduated in 2006. From then until July 2007, she worked in the Executive Council of Vojvodina, in the Provincial Secretariat for Healthcare and Social Policy.
Her career in the political life of Serbia began in 2000. She became a member of the Alliance of Vojvodina Hungarians (SVM). Since 2006, she has been a member of the presidency of the Youth Forum of this, the strongest Hungarian minority party.
In 2005, she joined the team of regional coaches of the National Democratic Institute.
Since mid-2007, she has been an MP in the National Assembly of the Republic of Serbia and in the Parliamentary Assembly of the Council of Europe. For several parliamentary legislatures, she has been a member of the Committee on Human and Minority Rights and Gender Equality, as well as the Committee on the Rights of the Child. In the 11th legislature she was the Deputy Chairperson of the European Integration Committee and deputy chair of the Stabilisation and Association Parliamentary Committee. From January 2018 to January 2020 she was the Chairperson of the Committee on Equality and Non-Discrimination of the Parliamentary Assembly of the Council of Europe. In the last legislature, she was a Deputy Speaker of the National Assembly of the Republic of Serbia and the Chairperson of the European Integration Committee, as well as a member of the Foreign Affairs Committee. Since January 2022 she has been a Vice-President of the Parliamentary Assembly of the Council of Europe (PACE).
For a long time, the Alliance of Vojvodina Hungarians did not have a Women's Forum. The founding assembly of the SVM Women's Forum was organised in 2009 and Ms. Kovacs was elected its president. In 2013, she was re-elected and remained in that position until 2015, when she became the vice-president of the Alliance of Vojvodina Hungarians. In 2019, she was re-elected vice-president of the party.
In addition to her native Hungarian and Serbian, she is also fluent in English and speaks German at an intermediate level.
Married, mother of one son.