Arthur Greene received an AB from Syracuse University in 1964 and an LLB from Boston University in 1967. He joined the law firm of McLane, Graf, Raulerson & Middleton in 1967 and became a partner in 1974. Arthur established a statewide trial practice, which focused on land use litigation, tax abatement appeals, environmental litigation, business disputes and personal injury cases. The firm grew from thirteen lawyers to seventy-seven lawyers in four statewide offices. He was involved in the management of the law firm from 1980 to 1992, serving during those years as a member of the Management Committee and as Managing Partner for a three-year term from 1985 to 1988. In 2000, he established a small law firm in which he practiced for a number of years. Arthur Greene has lectured and conducted workshops; and, written articles and books on a variety of law firm issues, including Trends in the Profession, Responding to Client Demands, Implementing Alternative Billing Methods, Marketing, Leveraging with Legal Assistants, Associate Training and Career Development, Creating and Organizing Effective Practice Groups, Evaluating Solutions to Financial Challenges, Trends in Partner Compensation, Affecting Change in the Law Firm Culture, Succession Planning and Preparing Your Lawyers for the Future. In 2013, a book on succession planning was publsihed, entitled Succession Plans for Law Firms and Rewards for Retiring Lawyers.

For many years, he served as Adjunct Professor at the New Hampshire University School of Law teaching a three-credit course in Law Practice Management to third-year students.

Arthur Greene is a long standing member of the American Bar Association and has served in many capacities in the ABA's Law Practice Management Section, including Past Chair of the Section and present Finance Officer and Liaison to the ABA Commission on the Billable Hour. He is also Past Chair of the ABA Standing Committee on Legal Assistants. He is past Chair of the New Hampshire Bar Association's Law Practice Management Section and a Past Task Force Member of the Bar's Future of Law Practice Task Force. He has served on the Advisory Board of the Legal Assistant Management Association; is a Past Committee Member of the Conference Committee of the Association of Legal Administrators and is a Fellow of the College of Law Practice Management.