新しい, 古い, and 若い: newness and age
Distinguish a newly acquired item from an old one, and examine human age with 若い and 年を取る rather than treating 古い as a general word for elderly.
What is new
新しい靴を買いました。 says that someone bought new shoes. 新しい, read あたらしい, can describe something recently made or newly brought into use.
新しい先生が来ました。 says that a new teacher has arrived. It means new to the setting, not necessarily young.
Distinguish age from wear
この建物は古いですが、きれいに保たれています。 says that the building is old but well maintained and clean. 古い, read ふるい, does not always imply damage or dirt.
古い友人から連絡がありました。 says that an old friend got in touch. It concerns a longstanding friendship, not necessarily the friend's advanced age.
Talk about a person's age
母は若いころ、この町に住んでいました。 says that the mother lived in this town when young. 若い, read わかい, describes a young age or life stage.
祖父は年を取っていますが、元気です。 says that the grandfather is older but healthy and energetic. Simply substituting 古い人 to describe age can change the meaning or impression.
Must a 新しい先生 be young?
Show the answer and why
No. The teacher may be new to that school or class. Newness and age are separate criteria.