Albert Barnes Commentary 1 Samuel 20:14-15

"And thou shalt not only while yet I live show me the lovingkindness of Jehovah, that I die not; but also thou shalt not cut off thy kindness from my house for ever; no, not when Jehovah hath cut off the enemies of David every one from the face of the earth." — 1 Samuel 20:14-15 (ASV)

The general meaning is this: Jonathan had an intuitive sense, doubtless from God, that David would be established on the throne. By God's mercy, he had the well-deserved comfort of knowing that his own descendants would receive kindness from David (see the marginal references).