There can be no standard answer to this question. The ultimate perspective is, of course, what Hosea did with his adulterous wife, Gomer. He remained with her, choosing to express his covenant love, even though she was a perpetual adulterer. God brought her to the place of repentance and Hosea was honored for his commitment.
Having said that, many who have an unrepentant, sexually sinful marriage partner choose not to remain in the relationship. And if they choose not to remain in the marriage, God will allow them to divorce their spouse. What the innocent spouse must do is appeal to the leadership of their church for the elders’ biblical wisdom on both the nature of the unrepentant spouse’s relationship to Christ, as well as the pattern of the sin and any church discipline, which would be involved, to take its course.
If the sinful spouse is not a professing believer, the innocent spouse should choose to show Christ’s love for sinners, but should they choose instead to divorce, it should be carried out with the full knowledge and allowance of their spiritual overseers.
Grace to You