Is the entire Old Testament the Old Covenant?

Or is it the Mosaic Law that is the Old Covenant (i.e. sacrifices, burnt offerings)? Hebrews 8:13 says that the Old Covenant is obsolete. If the verse refers to the entire Old Testament, that would mean NONE of the old testament would apply to Christians. That would mean several popular verses like Prov. 3:5-6, Psalms 37:4, and Jeremiah 29:11 are passages Christians don't have to follow. It especially means we can't praise God with instruments or tithe. Does anyone know what the writer of Hebrews was saying when he said, "He has made the first (covenant) obsolete?"