tablet, public notice, register
牓 centers on a flat surface used for public display: a tablet, board, or register for posting notices or recording information.
牓 combines 片 (a split piece of wood, often used for tablets or boards) with 旁, which likely contributes the sound ホウ and may reinforce the idea of a flat surface or side. The character is used for wooden tablets or public notices.
The left side 片 is a wooden board, and the right side 旁 looks like a notice posted on a wall. Together they make a public notice board or register.
For ホウ, imagine a public notice board in a hall: hall -> ホウ, and the board displays the register.