godan verb (-ku), transitive verb
listen and remember; take mental note of
Used when you listen to something with the intention of keeping it in mind for later, without necessarily acting on it immediately. Often implies a passive or reserved stance.
彼の忠告を聞き置くことにした。
I decided to take his advice to heart.
その話は聞き置いておきます。
I'll keep that in mind.