noun which may take the genitive case particle 'no', noun
Used as a noun or no-adjective to refer to something that came before, such as a previous job, address, or version. Often contrasts with 現 (げん, current) or 新 (しん, new).
先の社長はとても厳しかった。
The former president was very strict.
先の住所から新しい住所に変更しました。
I changed from my previous address to a new one.
noun
first move; opening move
Used in board games like go and shogi to refer to the first move or opening play. Often appears in phrases like 先を打つ or 先手.
将棋では、先を取るのが有利だ。
In shogi, taking the first move is advantageous.
元 also means 'former' but is more common for people (元彼, 元社長) and implies a past state that has ended; 先 is more neutral and can be used for things like addresses or versions.
The kanji 先 means 'ahead' or 'previous'. The reading せん is the on'yomi, used in many compounds. The exact historical derivation of this standalone noun usage is uncertain, but it follows the general meaning of 'prior' or 'former'.