The Greek adverb axiōs means worthily, in a manner worthy of, fittingly, in a way that befits. From axios (G514, worthy/deserving), it describes conduct that matches, corresponds to, or is appropriate for a given standard or identity.
Paul's use of axiōs is consistently tied to the gospel and the calling of God. 'Walk worthy (axiōs) of the calling you have received' (Ephesians 4:1). 'Walk in a manner worthy of the Lord' (Colossians 1:10). 'Walk worthy of God who calls you into his kingdom' (1 Thessalonians 2:12). The adverb reveals a profound NT ethic: identity precedes behavior. We are not trying to become worthy through our walk — we are walking in accordance with who we already are in Christ. The indicative (you are called) grounds the imperative (walk accordingly). Axiōs living is not earning favor but expressing truth.