To keep a promise; to do what one has agreed or said one would do, preserving trust.
明日は必ず約束を守るよ。
I'll definitely keep my promise tomorrow.
彼は約束を守る人だから、安心して任せられる。
He's someone who keeps his promises, so you can trust him.
約束を守らないと信用を失うことになる。
If you don't keep promises, you'll lose people's trust.