As an adjective:
* It describes something related to diplomacy, such as a diplomatic mission, a diplomatic corps, or a diplomatic solution.
* It can also describe someone who is tactful and skilled in handling delicate situations, like "a diplomatic response."
As an adverb:
* It modifies a verb or adjective to indicate that something is done in a tactful and skillful way, like "He handled the situation diplomatically."
So, the specific part of speech depends on its use in a sentence.