Tam Mahu Omer:
‘m not sure that there is a chiyuv to become a talmid chacham per se. But there is a mitzvos asei called Talmud Torah. The chiyuv of this mitzvah is all day. For every moment that a person isn’t learning he’s being mevatel this mitzvah unless:
1)he is doing a different mitzvah (osek b’mitzvah patur min hamitzvah)
or
2)he is doing something that will make him be able to learn (hechsher mitzvah)- this can (but doesn’t have to) include working in order to support one’s own learning, relaxing in order to have energy for learning and (almost) anything else that will help a person be able to learn.
This mitzvah is incumbent on all men ages 13 and up.
So even though there is no mitzvah to become a talmid chacham there is still a mitzvah to always be learning.
For more info see the sefer “Binyan Olam”
EDIT: Forgot to mention- there is also a lav on forgetting the Torah you learned but there are a few opinions on whether that is applicable now or was meant for before torah she’ba’al pe was written down. Chazarah though probably won’t hurt.