Purim is the celebration of God's deliverance of the Jews during the time of Queen Esther and Mordecai. Esther 9:27 explains that "the Jews established and imposed it [this celebration] upon themselves and their descendants." The following verse adds that this celebration was "to be observed among the Jews."
Purim is not a celebration commanded by God. It is a day of thankfulness established by the Jews themselves. Along similar lines, the United States established Thanksgiving as a holiday to thank God for His blessings. It is not wrong to observe Purim or Thanksgiving. Many Jews continue to observe Purim and many Americans observe Thanksgiving. But God doesn't command us to observe either. The days God commands us to observe are listed in Leviticus 23 and include the weekly Sabbath and the annual Holy Days.
As for the Old and New Testaments, we obey God's instructions in both. In 2 Timothy 3:16-17 Paul tells us, "All Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be complete, thoroughly equipped for every good work."
There have been some administrative modifications of God's instructions from the Old Testament, such as a change in sacrifices, to whom we should tithe, etc. These modifications, however, are explained in the New Testament. It is not Jesus' desire for us to simply ignore anything that comes from the Old Testament. He specifically said that He did not come to destroy the law or prophets (Matthew 5:17). When Jesus spoke this, He was clearly referring to the Old Testament. The New Testament did not come into existence until many years later.