网友核查一下，是不是抄错了句子。应该是漏掉了一个单词 as：

A king's time is as ruler rises and falls like the sun.

这样的话，as 用作连词，引导表语从句，类似 like, as if 的用法。但与这两个连词比起来，as 的比较意义更加真实和确切。ruler 省略冠词。rises and falls 是从句的谓语动词，like the sun 是从句的状语。

A king's time is as ruler rises and falls like the sun.

国王的时代如同统治者像太阳那样沉浮和盛衰。