With a Master's Degree in Economics, Eustace also has a lengthy record of international service. In 1977 he Joined the Caribbean Development Bank (CDB) as Administrative Officer. In 1983 he was promoted to Senior Manager, Project Services – responsible for the coordination of the Bank’s Technical Assistance Programme of some US $4m per year. In 1985 he returned to St. Vincent and the Grenadines on secondment from the Bank as Director of Finance and Planning, in the then new, NDP Government. He led and coordinated changes to the Government financial system that have contributed to stability of Government finances and the current account surplus achieved every year since 1985 to the present day. In 1993 Eustace resigned from the Bank and assumed duties as Fiscal Adviser to the Ministry of Finance. He was also assigned to play a lead role in the revival of the Banana Industry. 1995 – 1998 Eustace was Chairman of the Windward Islands Banana Development and Exporting Company Limited (WIBDECO). The Company was charged with the restructuring of the Windward Islands Banana Industry, leading the way for the promotion of improved competitiveness in the Industry.

1996 – 1998 Eustace was Chairman of the Joint Venture Holding Companies. He was integral in developments that led to Windwards Islands’ ownership of the production, shipping, ripening, marketing and distribution of bananas after nearly 50 years as mere producers.

1996 – 1998 Eustace was Chairman of the National Insurance Scheme (NIS). Leading the restructure and improvement of its performance and financial soundness. 

1996 - 1998 Eustace was Government Director on the Board of the East Caribbean Group of Companies (ECGC), the primary manufacturing facility in St. Vincent and the Grenadines and serving the OECS region.

1998 – Oct. 2000 Eustace was appointed Minister of Finance and the Public Service after being successful at the polls in the 1998 General Elections.

In October 2000 he was appointed Prime Minister of St. Vincent and the Grenadines after James Fitz-Allen Mitchell retired. He served as Prime Minister for five months, until the New Democratic Party lost the 2001 elections. He was then appointed Leader of the Opposition in the House of Assembly of Saint Vincent and the Grenadines. Since 1998 Arnhim has been the Parliament representative for the East Kingstown Constituency.

He has been responsible for constitutional reform within the NDP, widening the process for selection of candidates to be determined by not only executive members of the party but to include delegates to convention, central committee, youth arm and women's arm representatives.