Learn Turkish: Bu niteliği kazanmış olan adaylar yarın başvuracak. - The candidates who have gained this qualification will apply tomorrow.

While kazanan means 'who gain' or 'who are gaining,' using kazanmış olan explicitly shows that the gaining happened in the past, before the applying. The structure verb + -mIş olan acts exactly like the English present perfect ('who have gained'), highlighting a completed action whose result is a current condition for the candidates.

Why is nitelik (qualification) in the accusative case as niteliği?

Even though it is embedded inside a relative clause, the verb kazanmak (to gain) still requires its direct object. Because the object is specific—indicated by the word Bu (this)—it must take the specific accusative suffix -i (which also softens the final k to ğ).

Should we say kazanmış olanlar since the candidates (adaylar) are plural?

No. In this sentence, kazanmış olan acts as an adjective phrase modifying adaylar. In Turkish, modifiers do not take plural suffixes to agree with the noun they modify. You would only use kazanmış olanlar if you dropped the word adaylar entirely to mean 'those who have gained'.

Since adaylar (candidates) is plural, why isn't the final verb pluralized as başvuracaklar?