Promises should be properly carried out.

Literal

Promise [topic-は] properly fulfill-[should-べきだ].

きちんと is a highly useful adverb meaning 'properly, neatly, thoroughly' — related to the 擬態語 family but functioning as a regular adverb. It conveys carefulness and completeness, often with a moral/diligent flavor. 果たす ('fulfill') pairs naturally with 約束 as a slightly more formal alternative to 守る.