Apostolicity is a subject of much disagreement. Some traditions hold to a specific form of apostolic succession. Barth
refutes this as external, insufficient, and false.
For Barth, apostolic means the community listens to and is subject to the Scriptures. Through the Word, the Holy Spirit works and brings the Church into alignment with the work and will of God.
As such, apostolicity is the concrete measure of the other three marks. We cannot know whether a specific church is one, holy, and catholic outside of its following or not following the Scripture.
Here is his summary from page 712 of IV.62 (peruse an excerpt here)
Una describes its singularity. Sancta describes the particularity which underlies this singularity. Catholica describes the essence in which it manifests and maintains itself in this particularity and singularity. And finally, apostolica does not say anything new, in relation to these three definitions, but describes with remarkable precision the concrete spiritual criterion which enables us to answer the question whether and to what extent in this or that case we have or have not to do with the one holy catholic Church.
