Learn German: Der Vertreter übt Kritik an der Entscheidung. - The representative criticizes the decision.

Kritik üben is a noun-verb support construction (Nomen-Verb-Verbindung). While kritisieren means the exact same thing, using Kritik üben sounds more formal, objective, and professional. You will frequently encounter these constructions in news reports, business meetings, and official statements.

Doesn't the verb üben usually mean to practice? Why is it used in this context?

You are right that üben commonly means to practice a skill, like an instrument or a sport. However, in certain formal combinations, it translates more accurately as to exercise or to exert. Therefore, Kritik üben literally means to exercise criticism. Another common example of this meaning is Druck ausüben, which means to exert pressure.

Why do we need the preposition an here, and what case does it trigger?

The phrase Kritik üben specifically requires the preposition an to introduce the target of the criticism. In this fixed construction, an always takes the dative case. Because Entscheidung is a feminine noun, the article changes to der, resulting in an der Entscheidung.

Since we are talking about a topic, could I use über instead of an for this sentence?