ἀποθανόντες ἐν ᾧ κατειχόμεθα = being dead in or to that character in which we were held in a state of subjection; ἀποθανόντες τῷ (or ἐν τῷ) παλαίῳ ἀνθρώπῳ ἐν ᾧ κατ.; cf. Joh 5:4 T. R., the only other instance of the passive in N.T. Cf. Polyb. iv. 51. 1, θεωροῦντες τὸν πατέρα … κατεχόμενον ἐν Ἀλεξανδρείᾳ. The old nature was the prison in which we, our true selves, were detained.
ὥστε δουλεύειν = so that we are still servants (pres.) but in newness of spirit etc. Cf. Burton, §§ 369 f.
ἐν καινότητι πνεύματος. ἐν circumstantial. Our service is rendered in a new atmosphere marked by the presence in us of Spirit, i.e. the Spirit of the life in Christ Jesus; cf. Rom 8:1.
παλαιότητι γράμματος = the worn-out system which was marked by the dominance of written precepts. Cf. Rom 2:29; 2Co 3:6; S. H. Rom 2:27. The antithesis occurs only in these passages; and contrasts the external law with the internal quickening spirit.