Bishops grant faculties to presbyters and deacons to teach and preach in their name. Every cleric must have faculties from their bishop to licitly preach.
A thoughful answer was just posted, especially in relating the ministry of the Word back to the bishop, and I would only add a clarifying remark regarding the question of faculties.
In canon 764, the law itself gives priests and deacons the faculty to preach licitly unless restricted or revoked in some way: “With due regard for the prescription of can. 765, presbyters and deacons possess the faculty to preach everywhere, to be exercised with at least the presumed consent of the rector of the church, unless that faculty has been restricted or taken away by the competent ordinary or unless express permission is required by particular law.to preach by law.”
So particular legislation could require permission in addition to the faculty given in law. As well, a competent ordinary could restrict the preaching of a particular individual. Otherwise, though, the faculty is in the law itself.
However, canon 765 adds: “Preaching to religious in their churches or oratories requires the permission of the superior who is competent in accord with the norm of the constitutions.”
While sacred power is attached to the Sacrament of Orders, preaching is part of the teaching function rather than the sanctifying function of the Church (the third function being the governing function). In reality, the two functions overlap in the sense that the Church teaches when she sanctifies and teaches by sanctifying. (There are better ways to say that, though.)