12 To the rest I say this (I, not the Lord): If any brother has a wife who is not a believer and she is willing to live with him, he must not divorce her. 13 And if a woman has a husband who is not a believer and he is willing to live with her, she must not divorce him. 14 For the unbelieving husband has been sanctified through his wife, and the unbelieving wife has been sanctified through her believing husband. Otherwise your children would be unclean, but as it is, they are holy. 15 But if the unbeliever leaves, let it be so. The brother or the sister is not bound in such circumstances; God has called us to live in peace. 16 How do you know, wife, whether you will save your husband? Or, how do you know, husband, whether you will save your wife?—1 Cor. 7:12-16 NIV
If a Christian should decide to marry a non-Christian, the Christian is bound to those vows and must remain faithful to the non-believer. The unbeliever may choose to leave, in which case, the believer should allow them to go. Certainly it would have been better if the Christian had followed the advice to “not be unequally yoked” .
14 Do not be yoked together with unbelievers. For what do righteousness and wickedness have in common? Or what fellowship can light have with darkness?– 2 Cor. 6:14 NIV
The believer can grant the divorce to the unbeliever and is no longer bound to that person. We should let them go in peace. Are we then free to marry someone else? That is a question that you need to address to the Holy Spirit and follow His leadership.
12 Therefore, my beloved, as you have always obeyed, not as in my presence only, but now much more in my absence, work out your own salvation with fear and trembling; 13 for it is God who works in you both to will and to do for His good pleasure.–Phil. 2:12,13 NKJV
8 Now to the unmarried and the widows I say: It is good for them to stay unmarried, as I do. 9 But if they cannot control themselves, they should marry,for it is better to marry than to burn with passion. 10 To the married I give this command (not I, but the Lord): A wife must not separate from her husband. 11 But if she does, she must remain unmarried or else be reconciled to her husband. And a husband must not divorce his wife..—1 Cor. 7:8-11 NIV
Paul feels that his not being married gives him more freedom and more time to serve the Lord. He says that it would be good if you would stay unmarried unless this would cause you to commit the sin of sex outside of marriage. If you desire intimate companionship and children, then you should marry a Godly person. But once you make that commitment, you must remain faithful to that one spouse. God would prefer that we not divorce at all, but He gave us free wills and He knew that we would do that. Paul is writing a short paraphrase of what Jesus told the Pharisees in Matthew 19.
7 “Why then,” they asked, “did Moses command that a man give his wife a certificate of divorce and send her away?”
8 Jesus replied, “Moses permitted you to divorce your wives because your hearts were hard. But it was not this way from the beginning. 9 I tell you that anyone who divorces his wife, except for sexual immorality, and marries another woman commits adultery.”—Matt 19:7-9 NIV
Notice that when Jesus answers, He replaces the word “commanded” with the word “permitted”. Because of our free wills, God will not force anyone to stay married, but He would prefer that we allow Him to show us how to forgive and forget.