翁 is a classical/literary suffix meaning 'old man' or 'man of a certain type'. It appears in common compounds: 富翁 (rich man), 老翁 (old man), 渔翁 (old fisherman), 不倒翁 (roly-poly/tumbler toy).
羽 (the feather radical) sits below - historically depicting the white tuft of feathers under a bird's neck or at its throat. Applied to a person, the white feathers become white whiskers - the unmistakable sign of an elderly man, hence 翁.
公 supplies the sound (drifted from gōng to wēng) and almost all of the meaning - 公 already means venerable elder, grandfather, sir. 翁 sharpens this to specifically the elderly man image, layering feathers on top of the elder.
