Contradiction with Deuteronomy 4:2
This verse warns against adding or taking away from God's commandments, which contradicts with the introduction of a new song by Moses in Deuteronomy 31:22.
Deuteronomy 4:2: Ye shall not add unto the word which I command you, neither shall ye diminish [ought] from it, that ye may keep the commandments of the LORD your God which I command you.
Contradiction with Revelation 22:18-19
These verses warn against adding to or taking from the words of prophecy, a concept that could be seen as contradictory to the creation of new instructions or songs as mentioned in Deuteronomy 31:22.
Revelation 22:18-19: For I testify unto every man that heareth the words of the prophecy of this book, If any man shall add unto these things, God shall add unto him the plagues that are written in this book:
Contradiction with Proverbs 30:6
This verse advises not to add to God's words, similar to the potential view of Deuteronomy 31:22 as introducing something new.
Proverbs 30:6: Add thou not unto his words, lest he reprove thee, and thou be found a liar.