From 野(の) (no) + 締(し)め (shime, 連(れん)用(よう)形(けい) (ren'yōkei, “stem or continuative form”) of the verb 締(し)める (shimeru).). The jime changes to shime as an instance of rendaku (連濁).
のじめ • (nojime) ←のじめ (nozime)?