Please check my work.
Correctly identifying the part of speech of each of the word in the sentence.
The new mail carrier finally arrived.
The (definite article) new (adjective) mail (noun) carrier (noun) finally (adverb) arrived (past tense verb).
4 answers
I'd call "mail carrier" a noun -- it's a compound noun.
http://grammar.ccc.commnet.edu/grammar/compounds.htm
The word "mail" is a noun or an adjective in the sentence?
http://www.jiskha.com/display.cgi?id=1311122906