If you bought life insurance on your husband, and you get divorced, you can keep the life insurance.
If you got divorced and want to get life insurance on your ex-husband, you need his permission and signature on the application, and he may have to answer some health questions or even take a paramed exam which is paid for by the life insurance company.
You can insure your spouse, parent, sibling, relative, business partner, or anyone you have an insurable interest in. This means, if you stand to lose financially by the death of a person, or you rely on that person for financial support, you have an insurable interest in that person and may buy life insurance on him/her, with the person's permission/approval and signature.
Here's an article that provides more information on Who can you insure for life insurance?