The first, and simplest, recommendation is to prepare and execute updated will or trust documents for you and your current spouse to ensure that each of you are protected. In addition to providing for your current spouse, you want to consider any children you have with your previous spouse or in this relationship, and specify any bequests for their personal care or use in the event of your passing. Your estate plan should include distributions for both your current spouse, and your children, as well as ensure any obligation you have from your first marriage are also satisfied. This more then likely means ensuring that any life insurance obligation you have from your first marriage are up to date, do not have any liens or loans taken against them and that they continue in effect with all premiums paid in a timely fashion. Otherwise, your first spouse may have a claim against your estate, which will disrupt the updated plans you have for your children and current spouse.
The second recommendation, is to update all beneficiary designations on your retirement accounts, to ensure that those accounts pass, outside of your will, to the appropriate persons. Whether this be your children from this or a prior marriage, or to your current spouse. You want to ensure those designations have been updated upon the division of those accounts, in the event this was agreed to upon divorce, or if you establish new accounts after marrying your current spouse.
The third recommendation is to update your medical directive and power of attorney documents to reflect either your current spouse or adult children to make decisions on your behalf, instead of leaving old documents which do not reflect your present requests or preferences. You want to make sure that your current spouse and not an ex-spouse is in control of your money or health related decisions in the event of your incapacitation. This could leave your children and current spouse powerless to assist you in a particularly hard time.