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 Centre for Settlement of Investment Disputes (ICSID), the United Nations Commission on International Trade Law (UNCITRAL), the International Chamber of Commerce (ICC), the London Court of International Arbitration (LCIA), 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 2019 listing, Who's Who Legal ranked Ms. Brown de Vejar among the top two most highly regarded arbitration practitioners in Mexico, as well as a "thought leader," with respondents describing her as "an extremely dedicated and capable" attorney. In 2020, Ms. Brown de Vejar is listed among WWL's highly-regarded arbitration practitioners globally and in Mexico, with respondents describing her as "a great lawyer" and "super-smart younger partner." WWL said Ms. Brown de Vejar as well versed at representing private corporations and sovereign states in international commercial and investment arbitrations.” In the 2017 edition of Legal 500 Latin America, sources praise her as "one of the best in investment arbitration." Ms. Brown de Vejar was named one of the top 100 female lawyers in Latin America by Latinvex in 2017, 2018 and 2019, and in July 2018, Law360 recognized her as a Rising Star in international arbitration.

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.