Not only should we interpret New Testament scriptures in the light of the Old Testament, we should always interpret Old Testament scriptures in light of the New Testament. For example, some sincere believers have read the dietary laws of Moses and concluded that Christians should restrict their diets in accordance with those laws. If they would read just two passages in the New Testament, however, they would discover that Moses’ dietary laws are not applicable to those under the New Covenant:
And He [Jesus] said to them, “Are you too so uncomprehending? Do you not see that whatever goes into the man from outside cannot defile him; because it does not go into his heart, but into his stomach, and is eliminated?” (Thus He declared all foods clean) (Mark 7:18-19).
But the Spirit explicitly says that in later times some will fall away from the faith, paying attention to deceitful spirits and doctrines of demons, by means of the hypocrisy of liars seared in their own conscience as with a branding iron, men who forbid marriage and advocate abstaining from foods, which God has created to be gratefully shared in by those who believe and know the truth. For everything created by God is good, and nothing is to be rejected, if it is received with gratitude; for it is sanctified by means of the word of God and prayer (1 Tim. 4:1-5).
Under the new covenant, we are not subject to the Law of Moses, but to the Law of Christ (see 1 Cor. 9:20-21). Although Jesus certainly endorsed the moral aspects of Mosaic Law (thus incorporating them into the Law of Christ), neither He nor the apostles taught that Christians are obligated to keep the Mosaic dietary laws.
It is clear, however, that the early Christians, all converted Jews, continued to keep the old covenant dietary laws because of their cultural convictions (see Acts 10:9-14). And as Gentiles began to believe in Jesus, the early Jewish Christians asked them to limitedly follow Mosaic dietary laws purely out of deference to neighboring Jews who might be offended otherwise (see Acts 15:1-21). Thus, there is nothing wrong with Christians keeping the dietary laws of Moses just as long is they aren’t trusting that keeping those laws is what saves them.
Some of the early Christians were also persuaded that it was wrong to eat meats that had been sacrificed to idols. Paul instructed believers who thought otherwise (like himself) to walk in love towards their brethren of “weaker faith” (see Rom. 14:1), doing nothing to cause them to violate their consciences. If a person abstains from eating foods out of conviction before God (even if those convictions are unfounded), he is to be commended for his devotion, not condemned for his misunderstanding. Likewise, those who abstain from certain foods out of personal conviction should not pass judgment on those who don’t abstain. Both groups should walk in love towards the other, as this is certainly commanded by God (see Rom. 14:1-23).
In any case, because the Bible is progressive revelation, we should always interpret the oldest revelation (the Old Testament) through the light of the newest revelation (the New Testament). None of the revelation that God has ever given is contradictory; it is always complimentary.