While she was in her fourth year of college, she worked for the Office of Planning and Budget.[6] From March 1995 to December 1996, she served as a collaborator at BGV Corredores de Bolsa, and from 1998 to 2000 at the Center for Economic and Financial Research in Santiago.[7]
In 2001 she joined the Macroeconomic Advisory of the Ministry of Economy and Finance, at the request of her former professor ant then minister Isaac Alfie.[8] In that position, she participated in the design and implementation of measures against the 2002 crisis, and in the restructuring process of the total government debt in May 2003.[7][9] From 2005 to 2010, she served as an advisor to the Debt Management Unit of the Ministry of Economy and Finance, at the request of then-minister Danilo Astori.[8] She was its head from 2011 to 2014, when she resigned to join the presidential campaign of Luis Lacalle Pou as economic adviser.[10]
A member of the National Party, Arbeleche was in charge of economic issues for the presidential campaigns of Luis Lacalle Pou in 2014 and 2019.[12][13] On December 16, 2019, she was formally announced by the president-elect Lacalle Pou as head of the Ministry of Economy and Finance, becoming on March 1, 2020, the first woman to hold the position.[14][15] During the process of reactivating the Uruguayan economy as a result of the COVID-19 pandemic, Arbeleche expressed her admiration for Keynesian economics.[16]
With her husband Juan Alzugaray, Arbeleche has two sons born in Chile and a daughter born in Boston.[18][19] She is a Roman Catholic and has done social work as a catechist and teacher in slums.[20][6]
In 2014 she was featured on the cover of the magazine Seis Grados of the newspaper El Observador.[21]