Bishop Zammit was born in Gudja, south Malta, in 1949 and was ordained to the priesthood in 1974. In 1976, along with other young Maltese priests he was invited, by Bishop Rapallo, to minister in Gibraltar.
He served the Diocese in a number of different capacities from 1976 to 1998. He taught and served as Chaplain to both Boys and Girls Comprehensive Schools. He served as Parish Priest in two of the parishes in Gibraltar, St Theresa’s from 1985 to 1991 and Sacred Heart Parish from 1991 to 1998.
He was also Chaplain to a number of different organisations in the Diocese; as Bishop’s delegate on the Religious Education Board for Government Schools, and as a member of the Prison Board and Prison Chaplain.
In 1998, he returned to his native Malta, where he was appointed Chancellor of the Archdiocese of Malta and served the Archdiocese in a number of key roles until his appointment as Bishop of Gibraltar on 24 June 2016.