I have read that the prescribed duties of brahmin are becomings priests, learning and teaching so I want to clarify this doubt.
See the following verse from the Manu Smriti:
10.75. Teaching, studying, sacrificing for himself, sacrificing for others, making gifts and receiving them are the six acts (prescribed) for a Brahmana.
In the Sanskrit Shloka, the word used, which is translated as "teaching", is adhyApanam. Now, even the word for a professor/teacher in Sanskrit will be adhyApaka or "one who does adhyApanam"
So, apparently yes.
As per Chapter 2 (Varnashrama Dharma) of Kurma Purana, there are six types of action that are recommended for brahmanas. These are
yajana (performing sacrifices),
yaajana (acting as priests at sacrifices),
dana (donation of alms),
pratigraha (receiving gifts),
adhyapana (teaching) and
It doesn't have the word Vedas specifically. Moreover, as per Varna Ashrama chapter of Brahma Purana,
In times of emergency, a brahmana is allowed to adopt the livelihoods of kshatriyas or vaishyas to earn a living.