Saul was obliged to take David permanently under his wing at court; he could hardly snub David or reject him. If he left him there, who knows but that people might rally round him, and he might be a challenge to Saul, and present himself ultimately as a rival ruler of the land.
We don't make covenants with each other today, for the simple reason that a covenant between all Christians already exists. If I am born again and you are born-again, we are fellow labourers in the kingdom of God. God has written a covenant between us; it's already there. All we have to do is honour it, and we are bound together like Jonathan and David to uphold each other's reputations, never to gossip about each other, to help each other, if necessary reprove each other, encourage each other, strengthen and assist each other. We are bound by the new birth, by being in the family of God together. The covenant is already there. Are we honouring it? That is the issue. Jonathan and David made a covenant, and they bound themselves to each other. This is really only a picture of what will exist between all believers.