Article IX: THE visible Church of Christ is a congregation of faithful men, in the which the pure Word of God is preached, and the Sacraments be duly ministered according to Christ's ordinance in all those things that of necessity are requisite to the same. Article XXIII: IT is not lawful for any man to take upon him the office of publick preaching, or ministering the Sacraments in the Congregation, before he be lawfully called, and sent to execute the same. And those we ought to judge lawfully called and sent, which be chosen and called to this work by men who have publick authority given unto them in the Congregation, to call and send Ministers into the Lord's vineyard. Article XXVI: ALTHOUGH in the visible Church the evil be ever mingled with the good, and sometimes the evil have chief authority in the Ministration of the Word and Sacraments, yet forasmuch as they do not the same in their own name, but in Christ's, and do minister by his commission and authority, we may use their Ministry, both in hearing the Word of God, and in receiving of the Sacraments. Neither is the effect of Christ's ordinance taken away by their wickedness, nor the grace of God's gifts diminished from such as by faith and rightly do receive the Sacraments ministered unto them; which be effectual, because of Christ's institution and promise, although they be ministered by evil men. Nevertheless, it appertaineth to the discipline of the Church, that inquiry be made of evil Ministers, and that they be accused by those that have knowledge of their offences; and finally being found guilty, by just judgement be deposed.
I don't know if I can help you there. What does your heart tell you, through the inspiration of the Holy Spirit, are the essential primary characteristics of a person chosen ontologically by God and selected by his people, to perform the functions of a New Testament Anglican priest? Does that help?
An Anglican priest has to be lawfully ordained as such in accordance with the rules (canons) of the Anglican Church. This is pretty much as recorded in various epistles in the NT. Theoretically this prevents unsuitable people; those with bad theology or bad character; from setting themselves up as priests. It doesn't always work.
I think your question is difficult to answer. It may be easier if you explain what you mean by "definition of an Anglican priest" and say why you want to know this. Then, perhaps, people will be able to answer the question you have.
From the Catechism: Q. What is the ministry of a priest or presbyter? A. The ministry of a priest is to represent Christ and his Church, particularly as pastor to the people; to share with the bishop in the overseeing of the Church; to proclaim the Gospel; to administer the sacraments; and to bless and declare pardon in the name of God.