Aassalam Alaikum. My question is: Should we memorize more only if we have acted upon it as the prophet's companions used to do as I am a student of knowledge trying to start seeking knowledge?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

There is no doubt that the method of the Companions is the best and most perfect, as Abu Abdur-Rahman As-Sulami said: “Those who taught us the Quran, like ‘Uthmaan ibn ‘Affaan, ‘Abdullaah ibn Mas‘ood and others, reported to us that if they learned ten verses from the Prophet they would not go beyond them until they learned the knowledge and actions that they comprised. They said: so we learned the Quran, knowledge and action altogether. Therefore, they would remain a long time memorizing one Surah (Chapter).”

However, this does not prevent one from memorizing the Quran according to the method which is customary today, as there are revealed texts that recommend memorizing the Quran in an absolute sense. The Prophet said: “One who is skilled in the Quran will be with the noble, honorable scribes and one who recites the Quran and falters in it, because of it being difficult for him, he will have two rewards.” [Al-Bukhari and Muslim]

Allah Knows best.