새로운 used for describing something which make someone feel fresh.
antonym is 오래된(antique,aged)
새 used for describing something which is newly made and nobody used it before.
antonym is 헌(used,word out)
In short,
새로운 means "fresh new"
새 means "brand new"
-새로 is an adverb. It means "newly"
e.g.
새로 지은 집
a newly-built house
새로 일을 시작하다
start a new job