Questions & Answers about Yeni mezun bugün iş arıyor.
It is two words: yeni + mezun.
Yeni means new/recent, and mezun means graduate or graduated. Together, yeni mezun is a very common expression meaning recent graduate or new graduate.
In this sentence, the whole phrase yeni mezun works as the subject.
Turkish does not have articles like a/an and the.
So: yeni mezun can mean the recent graduate or a recent graduate, depending on context. iş can mean job/work, again depending on context.
Turkish often leaves this kind of information to context instead of marking it with articles.
Turkish often does not use subject pronouns unless they are needed for emphasis or clarity.
Here, the subject is already stated as yeni mezun, so there is no need to add o (he/she/it).
Also, Turkish verbs usually help show the person, though in 3rd person singular the ending is often zero. In this sentence, the noun phrase itself makes the subject clear.