* Von Claire: This is the most literal translation, meaning "from Claire" or "by Claire" and works well if it refers to something created or authored by Claire (e.g., "Ein Buch von Claire" - A book by Claire).
* Durch Claire: This means "through Claire" or "by means of Claire" and would be appropriate if Claire was instrumental in something happening.
* Claire's: This is an acceptable option, particularly if it's a possessive (e.g., "Claire's painting"). In German this would be Claires. Note the lack of an apostrophe.
To choose the best translation, please provide the sentence where "By Claire" appears.