“嗅着气味追赶”可以翻译为“chase (someone/something) by following the scent” 或者更简洁地表达为 “track (someone/something) by scent” 。
例如：
The dog chased the thief by following the scent.（那只狗嗅着气味追赶小偷。）
The hounds tracked the fox by scent.（猎犬们嗅着气味追赶狐狸 。）