The Old Covenant scriptures still bear relevance in the sense that they bear witness to the New Testament to which Christ appealed to make the case for His Messiahship, and to which the Apostles also appealed to make their case for the Gospel Christ has commanded to be preached. They bear relevance in their historical importance and in the righteous and moral laws that the were not declared obsolete and were carried over into the New Testament. And the scriptures Paul said were "inspired by God and profitable for teaching, for reproof, for correction, for training in righteousness" are just as much so today as they were in his day.
None of the scriptures, be they of the Old or the New Covenant, should be treated as being any less relevant than the rest. They are all equally inspired and therefore all equally irrelevant. The Old Covenant no doubt expired upon the death and resurrection of our Savior; scripture clearly attests to that, but I will place no expiration dates on any of the scriptures where none have manifested themselves.