No, the New Covenant is, like the Old, with the Jews. It was offered to the Jews, but they rejected their King when He came, and now it's in the future.Then you appear to be in conflict with yourself Glory. Luke records the establishment of the Eucharist that Christ instituted with the Eleven at the Last Supper. This is not Old Covenant, Mosaic Law. And it is new. And the Lord says, "This is the New Testament".
So promoting Luke to this supposed high priest Theophilus, is the New Covenant, it's contained in Luke. In Acts 13 (while it's already quite long), there's no reason to think that basically the whole Gospel of Luke isn't also implied in that speech or sermon Paul spoke to his audience.
(I can read Acts 13 in a few minutes, but Paul was elaborating for a whole morning and afternoon probably, Luke just wrote down the main points of what Paul actually said to them those days, not every single word.)
Paul told them the New Covenant (remember Luke is included by implication in Acts 13) justifies and that the Old Covenant can't justify. This has to be the same thing Peter preached to Israel, otherwise it would run afoul of Paul's cursing of any 'Gospel' in conflict with his own, which we just saw in Acts 13, at least does not promote following the Mosaic law as if it justifies. He contradicts that idea unequivocally.
10 For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
11 And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.
During this age of grace, we are under a totally different dispensation. Neither covenant claimed the law justified, and Paul merely agrees with that. It is faith that justifies, and it's always been faith that justifies. Look at Abraham.