Are the Gospels of Matthew, Mark, Luke, and John related to the Old Covenant (Old Testament, Hebrew Bible)?

Are the Gospels of Matthew, Mark, Luke, and John related to the Old Covenant (Old Testament, Hebrew Bible) since the Testator (Jesus), who lived, preached, and performed miracles within it, had not yet died? Hebrews 9:16-17 King James Version > For where a testament is, there must also of necessity be the death of the testator. For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth.