Then when did Pentangeli enter the picture? When Michael visited him in NY, he said he was "very glad this house didn't go to strangers--first to Clemenza, then to you," implying a direct succession.
With Rocco in Nevada (instead of NYC, per the novel), Cicci provides NYC continuity between GF and II. As we know, FFC wanted Castellano to reprise Clemenza in II, but they couldn't come to terms. Hence Pentangeli, and Cicci as his subordinate.
The paucity of any reliable time frames in the novel or films makes answering some of these questions quite a challenge. However, I think this might work.
There's no evidence of Clemenza alive in GFII. Frankie is apparently already in charge in NY. Cicci and Frankie are wearing black armbands, so that's some indication that Clemenza's death was fairly recent and Frankie took over soon after - a direct succession.
Who took over from Frankie? I really cannot guess other than Cicci. As I posted above, we are not apprised of any other characters who could do so except Neri and Lampone who were cemented into their roles in Nevada.
