The people alive during the Old Testament had to believe in the coming messiah and follow rules such as circumcision, etc.
The New Testament mandate stipulated everyone had to believe the gospel: That Jesus was the promised Messiah who paid the price for the sin of all humanity through His death, was buried and resurrected. And after believing in the finished work of Jesus Christ they were instructed to repent, be water baptized in Jesus' name and receive the gift of the Holy Ghost. (Acts 2) The New Testament began when the Holy Ghost was poured out at Pentecost and applies to all those who have lived and died since then and until Jesus' second coming.
The following scriptures indicate that obedience to the gospel is not possible after death:
And as it is appointed unto men once to die, but after this the judgment: Heb 9:27
And hath given him authority to execute judgment also, because he is the Son of man.
Marvel not at this: for the hour is coming, in the which all that are in the graves shall hear his voice,
And shall come forth; they that have done good, unto the resurrection of life; and they that have done evil, unto the resurrection of damnation. John 5:27-29
Whatsoever thy hand findeth to do, do it with thy might; for there is no work, nor device, nor knowledge, nor wisdom, in the grave, whither thou goest. Eccl 9:10
And I heard a voice from heaven saying unto me, Write, Blessed are the dead which die in the Lord from henceforth: Yea, saith the Spirit, that they may rest from their labours; and their works do follow them. Rev 14:13