What are the details concerning a Cohen being allowed or forbidden to marry a woman who may have had sexual relations with somebody non-Jewish?
On account of the special status of Kohanim, they are prohibited to marry certain kinds of women, who are considered in some way ‘blemished’ (although we do not necessarily understand why, the Torah defines this as a spiritual blemish). One of these is a woman who has has sexual relations with somebody who is forbidden to her, including with a non-Jew (see Yevamos 61a). Therefore, a woman who has had sexual relations with a non-Jew may not marry a Kohen.
For all practical cases an expert authority must be consulted, because there are many factors that can influence the halachic ruling.