“建立外交关系”常见的英文表达是 "establish diplomatic relations" 。
例句：
The two countries decided to establish diplomatic relations to promote peace and cooperation in the region.（这两个国家决定建立外交关系，以促进该地区的和平与合作。）
It was a significant event when China and this African nation established diplomatic relations.（中国和这个非洲国家建立外交关系是一件具有重大意义的事件 。）