The phrase is four words long:
einer neueren Studie nach
The word "nach" is an apposition, that normally is used as a preposition:
nach einer neueren Studie
But it also can be used as a postposition as in your example.
The whole part of speech would be called a prepositional object (Präpositionalobjekt) if "nach" were the first word. I'm not sure if you call it a postpositional object here, but the grammatical function is the same.
The apposition "nach" is one of the prepositions that only can be used together with a complement in dative case. And in fact, "einer neueren Studie" is in dative case. You can see it, when you forget the attribute "neueren" for a moment:
"Die Studie" is a feminine word, so with an indefinite article it is:
Nom: Eine Studie wurde veröffentlicht.
Gen: Dieser Umstand bedarf einer Studie.
Dat: Diese Erkenntnis verdanken wir einer Studie.
Akk: Ich lese gerade eine Studie.
Now for the Attribute "neueren":
Most words that are used as attributes are adjectives, and this is true in this case too. And most adjectives can appear in three degrees of comparison, and the adjective "neu" (new) is one of them:
positive
Die Studie ist neu. The study is new.
Die neue Studie sagt, dass Wasser flüssig ist. The new study says Water is liquid.
comparative
Die Studie ist neuer. The study is newer.
Die neuere Studie sagt, dass Wasser flüssig ist. The newer study says Water is liquid.
superlative
Die Studie ist am neuesten. The study is newest.
Die neueste Studie sagt, dass Wasser flüssig ist. The newest study says Water is liquid.
All adjectives that are used as attribute inside a noun group must be inflected, as you can see in the examples above. And when you combine comparative and dative case, you get:
nach einer neueren Studie
according to a newer study
But in english this sounds not really satisfying, so you replace "newer" by "more recent" (which is the comparative of "recent"):
according to a more recent study
But this again doesn't sound like good English, so you don't use the comparative, but the positive form:
according to a recent study