"1 (not before noun
) ~ (in sth) taking part in sth; being part of sth or connected with sth: to be / become / get involved in politics We need to examine all the costs involved in the project first. We’ll make our decision and contact the people involved. Some people tried to stop the fight but I didn’t want to get involved. In this meaning, involved is often used after a noun.
2 (not usually before noun)
~ (in / with sth/sb) giving a lot of time or attention to sb/sth: She was deeply involved with the local hospital. I was so involved in my book I didn’t hear you knock. He’s a very involved father (= he spends a lot of time with his children).
3 (not usually before noun
) ~ (with sb/sth) having a close personal relationship with sb: They’re not romantically involved. You’re too emotionally involved with the situation.
4 complicated and difficult to understand complex: an involved plot"
The only sense which doesn't have "not (usually) before a noun" is the one you mentioned, i.e. convoluted, complicated.
Or you could think of it as "concerned", and there is an even clearer difference in meaning between "the concerned agency" and "the agency concerned".
Are you trying to convice another English native speaker, or a German translator?