The New Testament most certainly does address adultery and divorce - with the words of Jesus himself!
Matthew 19:7-9 (NKJV) They said to Him, “Why then did Moses command to give a certificate of divorce, and to put her away?” 8 He said to them, “Moses, because of the hardness of your hearts, permitted you to divorce your wives, but from the beginning it was not so.
9 “And I say to you, whoever divorces his wife, except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery.”
P.S. The Catholic Church would permit civil divorce but not remarriage unless the first marriage was found to be invalid.