The former Fine Gael deputy leader served as a TD for Cork for almost 30 years, and held many cabinet roles including Minister for Transport, Education and the Environment.
As Minister for Foreign Affairs, he played a crucial role in negotiating the Anglo-Irish Agreement in 1985.
He was also a major shareholder in the family business, Barry's Tea, and his daughter Deirdre Clune is a Fine Gael MEP.
Taoiseach Enda Kenny said Peter “gave outstanding service to his country and to his native city” throughout a “long and distinguished political career”.
President Michael D. Higgins described him as a person who was immensely popular across all parties and gained enormous respect internationally through his work in the family business.