Is it:
Throw shade. It's an expression recently added from American slang that made it into the dictionay last year I believe.
My prefix is unused clutter.
I do belive that before the edit you said something about a dumpster, but it qualifies anyways since unused clutter you throw away.
My suffix doesn't sound merely cool.
Shade is cool, colder than everything on the sun.
My infix doesn't tick or talk.
Since they are two words, the infix is a space, so it doesn't talk
I leave a lot to be desired (11).
"Throw shade" is eleven characters counting the space in between and also it can mean to express "contempt"
I leave a lot to be desired (11).
Does this mean the solution has 11 characters ? $\endgroup$