Due to her good performances in 2015 and 2016, she was included in the yearly list of best referees in the world by the International Federation of Football History & Statistics (IFFHS).

She was born into a football family, since her father is a coach, her maternal grandfather was a referee, and her uncle was a professional player who excelled in France, Rubén "Pico" Umpiérrez.

When she turned 18 and moved to Montevideo to study law, she heard on the news that enrollment to the referee school was open.

[8] In the following year she took part in her first international competition, being called to officiate in the South American U-17 Women's Championship.

Due to good performance, she was selected to be the referee of the third place match, on 11 February in São Paulo, between Paraguay and Venezuela.

At the end of March 2010, she was the designated referee of a Third Division match between Peñarol and Defensor Sporting at the Estadio Centenario.

She debuted in the official international club competition on 4 October 2010, as the referee in the Everton [es]-UPI match.

[16] Due to her good performances, she was assigned to a semifinal, played on 9 October between North Korea and Germany.

After a successful 2012, Umpiérrez passed a physical test, but was in fourth place at the end of the year among second category referees.

On 6 March 2013, she was recognized by the Minister of Tourism and Sport, Liliam Kechichián, as one of the pioneers representing the country in international women's refereeing.

On 4 March 2015, she was referee of the opening match of the international friendly tournament for women's teams, played between Japan and Denmark.

As the referee of the match between United States and Australia, she issued three yellow cards and the USA won 3–1.

[23][24] She was the referee again on 16 June, the last date of Group C. She gave five yellow cards in Cameroon's 2–1 victory over Switzerland.

[25] She was appointed to referee the quarterfinal match, between England and Canada, played on 24 June before more than 54,000 spectators at BC Place in Vancouver.

[26] In addition, Claudia was twice the fourth official, once in the World Cup Final, a match in which the United States defeated Japan 5-2 and won the title.

[28]After her World Cup experience, she returned to Uruguay and her work had a media impact, which left women well positioned.

[29] Claudia Umpiérrez passed the men's physical test, with the possibility of ascending from the second category[b] of referees to the first, and this was approved.

It was the first match of the Suat Cup [es] for the Miramar Misiones centenary, between Cerro Largo and Boston River.

She refereed an international friendly on 28 November, which was played at Pacaembu Stadium in São Paulo, between the national teams of Brazil and New Zealand.

On 1 March it was announced that the president of Peñarol, Juan Pedro Damiani, would invite Umpiérrez for the inaugural match of the club's stadium, in recognition of Women's Month.

She officiated in Parque Palermo before some 400 people, in a meeting between Central Español and Tacuarembó on the first day of the second round of the Second Division [es].

[47] History was made on 4 September 2016, when for the first time a woman was the central referee of a Uruguayan First Division match.

[56] She currently works at Banco de Seguros del Estado, and occasionally practices as a private attorney.