Is there a ktor-client plugin that adds set of default headers such as Date (counterpart to server plugin DefaultHeaders)?

Yes: https://ktor.io/docs/default-request.html

I found that, but there doesnt seem to be option to add Date header?

defaultRequest {
    header("X-Date", "${Instant.now()}")
}

You can use something like this. Or are you looking for something else?

I wanted standard Date header, I thought the client would add one by default https://developer.mozilla.org/en-US/docs/Web/HTTP/Headers/Date