The question asks to identify who among the given options was not an Acharya (teacher or scholar) at The Nalanda Vishvavidyalaya (University). Let's examine each option:

1. Shantirakshit: Shantirakshit was a renowned Buddhist scholar and a monk who played a significant role in the spread of Buddhism to Tibet. He was indeed associated with Nalanda University.
2. Nagarjuna: Nagarjuna is one of the most important figures in Mahayana Buddhism and was associated with Nalanda University. He made substantial contributions to Buddhist philosophy.
3. Sheelbhadra: Sheelbhadra was a renowned Buddhist scholar at Nalanda during the university's prime. He is known to have been an Acharya at Nalanda.
4. Kautilya (Chanakya): Kautilya, also known as Chanakya or Vishnugupta, was an ancient Indian teacher, philosopher, economist, and political strategist. He is traditionally identified as the author of the 'Arthashastra'. However, there is no historical evidence suggesting that Kautilya was ever associated with Nalanda University. His timeline precedes the establishment of Nalanda.

From the above examination, we can see that the correct answer to the question is:

Kautilya

Kautilya was neither a teacher nor associated with Nalanda Vishvavidyalaya, unlike the other figures mentioned in the options.