According to Catholics, what is the law placed within the Israelite in the New Covenant? In Jer. 31:31-34, it is written,


  31 “Behold, the days are coming,” said Yahveh, “that I shall cut a new covenant with the house of Israel and the house of Judah, 32 not like the covenant that I cut with their fathers in the day that I took their hand to bring them out of the land of Egypt, which covenant they broke, although I was a husband to them,” said Yahveh. 33 “But this shall be the covenant that I shall cut with the house of Israel. After those days,” said Yahveh, “I shall put My Law within them, and I shall write it upon their hearts, and I shall be their god, and they shall be My people. 34 And a man shall no longer teach his neighbor, and a man his brother, saying, “Know Yahveh!” for they all shall know Me, from the least of them even unto the greatest of them, for I shall forgive their iniquity, and I will no longer remember their sin.”


In the New Covenant, the prophet Jeremiah states that Yahveh shall put His Law within the Israelites and write it upon their hearts.

According to Catholics, what is this Law that Yahveh puts within the Israelites?
Here's what the Catholic Haydock Commentary says about those verses:

Ver. 31. Covenant. That made with the captives was not such. Their covenant is grown old, and at an end, as St. Paul shews, Hebrews viii. 8. They were not indeed divided, as they had been, Ezechiel xxxvii. 16.
Ver. 32. Dominion. As a husband, (Hebrew; Calmet) or &quot;Lord.&quot; (Haydock) --- &quot;I despised them.&quot; (Septuagint) (Hebrews viii.)
Ver. 33. Heart. They were more docile after their return: yet still their service was very imperfect and forced. How many false traditions were received, at the coming of Christ! This of course, regards his disciples.
Ver. 34. Lord. Christ himself came to instruct mankind. The true God was better known than ever, even by the illiterate. Yet God requires us to have recourse to men, in order to know his truths, as St. Paul was sent to Hananias, and the eunuch to Philip. [Acts viii., and ix.] (Haydock) --- The apostles were enlightened by the Holy Ghost, (John vi. 45.; St. Augustine, de Spir.; Calmet) who still guides the flock by his pastors. The private spirit is too fanatical and delusive. (Haydock) --- The most ignorant shall easily become acquainted with the truths of salvation. External preaching is requisite, though of little use unless grace touch the mind and the heart. (Tirinus) --- All will hear successively, (Haydock) or embrace the gospel at the same time, for several years before the last day. (Houbigant, pref. in Prop. 356) (Isaias xi. 9., and xlv. 23., and Sophonias iii. 9., &amp;c.) (Haydock)