Because "important" is capitalized there! An adjective is not usually capitalized in the middle of a sentence, unless it's been derived from a proper noun. If it were "important" rather than "Important", it would be correct too, though there would be a difference of meaning between the two versions, you see.
Ignoring the capital letter, "important" would sound odd in AE: "Maintaining leadership with our overseas agencies is one of your
important duties." The sentence is about one duty. Changing "duties" to "important duties" is either bragging ("look how important you are") or adding a new topic to the sentence ("also, some of your duties are important").
With "more important", the whole sentence is about this duty, and says it is a high priority duty.