After several rounds of sincere talks, the two countries finally re-established diplomatic relations.

re-established 是动词 re-establish 的过去式形式。re-establish 由前缀 re-（表示"再次"）和动词 establish（建立）组成，字面意思是"再次建立"。 re-established diplomatic relations 指的是"重新建立外交关系"，表示两国之前曾有过外交关系，后来中断，现在又恢复了这种关系。