In the post "Will another baby affect your current will?"New Jersey 101.5 advises checking on your will to see whether it identifies your "children" or "descendants" as your beneficiaries—and then defines those terms to provide that children born after you executed your will are included.
If it does, then it is probably not urgent to update your will to include your new child's name. However, if the will was drafted without that flexibility and only identifies your first child by name as the beneficiary, then you need to talk with your estate planning attorney and have your will updated.
While you're at it, review your beneficiary designations for your life insurance policies and retirement plans. In those documents, you may have named your first child specifically as a beneficiary. If so, an update may be necessary.
Also, be careful of naming your estate as the beneficiary of any retirement assets. If you do, it can have unintended adverse income tax consequences after your death.
If your estate includes significant assets, such as retirement accounts and trusts for your heirs, a new child in the family is also the time to sit down with your estate planning attorney to ensure that all of your wills and retirement account beneficiary designations are up-to-date and that tax planning has been optimized.
Reference: New Jersey 101.5 (January 12, 2016) "Will another baby affect your current will?"