If a Cohen had married a non-Jew, and divorces her (as in Ezra ch 9 & Ezra ch10) could he marry a virgin, unmarried Jewess? I am reading the Book of Ezra and am curious to see what would have been the next step after the Kohanim put away their non-Jewish wives and would any males born after have status of Kohanim?
Any "marriage" between a Jew and a non-Jew is invalid and regarded as never having happened. It is a sin but if the Jew does teshuvah and separates from the non-Jew, there is no "ceremony" required. That is, since it was never a "marriage" no "divorce" is required.
If the non-Jew was the "wife" then any children are also not Jewish at all.
In the case written in Ezra, as soon as the Jews who had intermarried sent away the nonJewish wives (and any children) then there was no relationship between them. Once he had sent them away, he was allowed to marry a permitted Jewish woman and their children would be kohanim.
The child of a kohen and a divorcee is a "chalal" and is not a kohen. In that case, the kohen must divorce her. However, if the kohen marries a permitted woman (widow for a regular kohen or virgin for a kohen gadol), then their children are kohanim. The reason is that the kohen does not lose his status as a kohen once he has left the forbidden woman.
A kohen may not marry a ge’rusha (divorcee), chalalah (woman of defective kohen status), zonah (woman who previously violated certain sexual prohibitions), giyoret (convert) or chalutzah (a Levirate widow). If he does marry any of them, their children likewise become chalalim. Sons born do not have priestly status, and daughter may not marry kohanim.
The kohen himself cannot have his priesthood removed. If he terminates the prohibited marriage, by death or divorce, he may resume his kohen privileges. There is no such thing as the "defrocking" of a kohen.