The second δέ of Luke 3:1 is interesting and puzzling.
The verse begins with δέ as you would expect, marking a new section of the narrative – a development in the story.
However, as Luke gives us some relevant Roman historical background, the doesn’t simply connect all the phrases with καί, but about halfway through the list, he conjoins two phrases with a second δέ.
Usually δέ is marked for discontinuity whereas in this instance, the context demands that continuity is present.
My understanding, as suggested by Culy et al., is that the δέ is functioning to break up the fairly long list of names. So it is a bit like a shadow of the initial δέ, sort-of-but-not-quite-resumptive. I don’t know if there’s a special title for this function (Culy doesn’t have a name for it!).
I think it’s functioning as if to say “Bear with me everyone, I know this is a long list of names, there’s a few more to come, but I promise that I do have a point in telling you all this…”
[ I am not convinced with how the BW8 Leedy diagram has taken this δέ. He has taken it pretty much as though it were a καί which joins the preceding and following clauses. ]