Kate Brown de Vejar focuses her practice on international commercial and investment arbitration. She has represented private corporations, sovereign states and state-owned entities in connection with international arbitrations under the leading institutional and ad hoc arbitration rules, including those of the International Chamber of Commerce (ICC), the London Court of International Arbitration (LCIA), the International Centre for Settlement of Investment Disputes (ICSID), the United Nations Commission on International Trade Law (UNCITRAL), the Mexican Chamber of Commerce (CANACO) and the Japan Commercial Arbitration Association (JCAA). Ms. Brown de Vejar also acts as an arbitrator.

Widely recognized for her experience handling complex, high profile disputes in the energy and infrastructure sectors, Ms. Brown de Vejar's experience also extends to disputes in the aeronautical, financial services, mining and satellite/telecommunications sectors. She is Vice-President of the LCIA's Latin American Users' Council, Co-Chair of the IBA's Subcommittee on Recognition and Enforcement of Arbitral Awards, a Board Member of CAIC (the Arbitration Center for the Construction Industry in Mexico), a member of the ICDR-CANACO Joint Committee, and Vice President of ANZMEX (the Australia, New Zealand, Mexico Business Council).

In its 2021 Global Arbitration ranking, Who's Who Legal (WWL) includes Ms. Brown de Vejar in the highest category of "Global Elite Thought Leader," and ranks her the No. 1 arbitration practitioner in Mexico, noting that she "is celebrated as 'smart and strategic' by observers who cite her impeccable track record in disputes across the mining, oil and gas, and construction sectors.” Legal 500 (2021) Latin America testimonials describe Ms. Brown de Vejar as “outstanding … our firm finds that her focus, insight and strategic direction are best in class. Every interaction is the very definition of professionalism.” Ms. Brown de Vejar has been named one of the top 100 female lawyers in Latin America by Latinvex in 2017-2020.

From 2008–2017, Ms. Brown de Vejar represented Australia, her country of origin, at the meetings of UNCITRAL Working Group II (Arbitration and Conciliation) and the Commission. In this role, she participated in the Working Group's 2010 and 2013 revisions to the UNCITRAL Arbitration Rules, the development of the UNCITRAL Rules on Transparency in treaty-based investor-State arbitration, the negotiation of the Mauritius Convention on Transparency, as well as the definition of the mandate for UNCITRAL Working Group III's current work on reform of investor-State dispute settlement.