Being then made free from sin, ye became the servants of righteousness.
Note 10 at Ro 6:18: Jesus said, "No man can serve two masters: for either he will hate the one, and love the other; or else he will hold to the one, and despise the other. Ye cannot serve God and mammon" (Mt 6:24). We cannot become the servants of righteousness until we are made free from serving sin.
As discussed in note 9 at Ro 6:16, "servants" here denotes slavery. Christians still sin (1Jo 1:7 and 9), but they aren't the slaves of sin (see note 9 at Ro 5:21) anymore. Those who believe that the "old man" still lives and exerts mastery in their lives (see notes 1-3 at Ro 6:11) will not experience the joy of being servants to righteousness.