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 in commercial matters, with particular experience in disputes under the Construction Rules of the American Arbitration Association.

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 a member of the Board of Directors of the Centre of Arbitration for the Construction Industry in Mexico (CAIC), and Vice President of ANZMEX, the Australia, New Zealand, Mexico Business Council. In its 2019 listing, Who's Who Legal ranked her as the second most highly regarded arbitration practitioner in, as well as a "thought leader," with respondents describing her as "an extremely dedicated and capable" attorney. 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 both 2017 and 2018, 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.