Although a staunch supporter of the Parliamentary cause during the English Civil War, Milton was nonetheless deeply unhappy with some of the political developments taking place under the new Commonwealth. In particular, he was disturbed by plans afoot in the Long Parliament for a radical change in the country's religious settlement.
A large number of Parliamentarians, as well as the Presbyterians of the Westminster Assembly, wanted to reform the Church of England so that it would resemble Calvinist churches in places like Geneva and Scotland. Under the proposed Presbyterian system of church government, the new Reformed Church would have the right to persecute and punish anyone it regarded as a sinner.
As a champion of religious liberty—for Protestants, at any rate—Milton was strongly opposed to such measures. He was an Independent, which meant that he believed that each individual congregation should have the right to determine how it worshiped. That being the case, he argued, no centralized church government should have the power to enforce religious belief.
As far as he was concerned, this was no better than how the Church of England had behaved under the former Archbishop of Canterbury William Laud, who had persecuted Presbyterians and other radical Protestants. This is what Milton means by "New Presbyter is but Old Priest writ large." According to him, the Presbyters of the new church government are even more intolerant and tyrannical than the priests of the old.