The hand radical (left-side form of 手) marks 擅 as something done by deliberate human action - a skill exercised, or an authority seized without permission. It sits with 操, 持, 扛 in the broader family of capable, controlling hand-actions.
Lends the sound, drifting from dǎn to shàn. It heads a small phonetic series with 颤 and 檀, all sharing this stem. The classical sincere meaning is unrelated; readers use 亶 here purely as a sound clue for an otherwise opaque character.
