According to the dictionary entry, the word 'regime' is (3.) a noun.
The word 'regime' is a noun and it is mainly used to refer to a particular system of government of a country. It usually has a negative connotation since it is associated with authoritarian governments. An example is: "The Nazi regime ended in 1945, the year in which Germany was defeated by the Allies". However, the word 'regime' can also be used to refer to an ordered way of operating and organizing things. It also functions as a noun in this sense.