不能换.As a condition of receiving state approval for the sale,这不是一个完整的句子,是条件状语从句.主句是the company agreed to seek permission from state regulators to operate past 2012.
如果你把of换成that,（As a condition that..）那么that后边接的应该是一个句子,实际上后边只是一个词组短语 （receiving state approval for the sale）,这样句子结构不完整,你要加上动词做谓语,有时候还要适当补上主语.
必须要换that的话,可以试试这么换：直接把As a condition of 换成On condition that,貌似这样就可以啦.
英语学得不好,如果有错误还希望大家能指出来大家一起进步.