expression, ichidan verb
to be cleared of suspicion; to have one's name cleared
Used when doubt or suspicion about someone is resolved, often in legal or personal contexts.
新しい証拠のおかげで、彼の疑いが晴れた。
Thanks to new evidence, he was cleared of suspicion.
More formal and specifically refers to being cleared of criminal suspicion or charges.
Composed of 疑い (doubt, suspicion) + が (subject marker) + 晴れる (to clear up, as of weather). The metaphorical use of 晴れる for dispelling doubt is well established.