Abarim Publications' online Biblical Greek Dictionary
The verb κλεω (kleo) isn't used in the Bible, but it's the root of the first part of names like Cleopas and Cleopatra. In Greek literature there is even a Muse called Κλειω (Clio, daughter of Zeus and Mnemosyne, or memory).
Our verb describes a verbal glorifying: to tell about someone, to forward one's fame, to propagandize. In the classics this verb also covered the discussion of men and gods in lyric poetry (since that is what theogonies were designed to do: to forward the fame of a deity by means of discussing his or her deeds).
The only Biblical derivation of our verb is the noun κλεος (kleos), which describes the fame, repute or renown purported by means of the verb. It occurs only once in the New Testament, namely in 1 Peter 2:20.