要说“The concert they given was a success"
的话,应是"The concert (that) they have given was a success".或
"The concert (that) they gave was a success".
这是定语从句的说法.“that they gave”是定语从句.
但分词状语的说法“The concert given by them was a success”更简洁.given是分词状语,修饰concert.