label, genealogy, circular
牒 centers on a flat piece of wood or paper used for recording or communicating information: a label, a written slip, or a genealogical record. The 'circular' sense extends this to a document circulated among people.
牒 combines 片 (a split piece of wood or a flat board) with 枼, which likely contributes the sound and the idea of thin, flat leaves or sheets. Together they suggest a wooden or paper slip used for writing labels or records.
The left side 片 is a flat board, and the right side 枼 looks like a tree 木 with leaves 世. Imagine a thin wooden label tied to a tree branch, recording family names for a genealogy chart.
For チョウ, imagine a long genealogy scroll labeled with the name 'Chou' (pronounced 'choh') at the top: Chou -> チョウ, and the label marks the family line.