Yes we are are under the law, though a different law than what the Israelites were.
James 2:12 KJB
"So speak ye, and so do, as they that shall be judged by the law of liberty."
The law of liberty is the law we are under.
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"On the phrase, "the law of liberty," see the notes at
James 1:25. Compare the notes at
James 4:11. The meaning is, that in all our conduct we are to act under the constant impression of the truth that we are soon to be brought into judgment, and that the law by which we are to be judged is that by which it is contemplated that we shall be set free from the dominion of sin. In the rule which God has laid down in his word, called "the law of liberty," or the rule by which true freedom is to be secured, a system of religion is revealed by which it is designed that man shall be emancipated not only from one sin, but from all. Now, it is with reference to such a law that we are to be judged; that is, we shall not be able to plead on our trial that we were under a necessity of sinning, but we shall be judged under that law by which the arrangement was made that we might be free from sin. If we might be free from sin; if an arrangement was made by which we could have led holy lives, then it will be proper that we shall be judged and condemned if we are not righteous. The sense is, "In all your conduct, whatever you do or say, remember that you are to be judged, or that you are to give an impartial account; and remember also that the rule by which you are to be judged is that by which provision is made for being delivered from the dominion of sin, and brought into the freedom of the gospel." The argument here seems to be, that he who habitually feels that he is soon to be judged by a law under which it was contemplated that he might be, and should be, free from the bondage of sin, has one of the strongest of all inducements to lead a holy life."‐ Barnes commentary on James 2:12