An individual may be exposed to a pathogen and become infected without actually getting sick. this is known as a subclinical infection. even in subclinical infections, the individual's adaptive immune system can generate memory for the pathogen. what type of adaptive immunity is this?

Naturally acquired active immunity

Explanation:

Naturally acquired active immunity occurs when an antigen comes naturally in the body and immune cells are produced against it which also generates memory against the pathogen. It can lead to disease or just cause a primary immune response in which host do not get sick.

Artificially acquired active immunity occurs when antigen is introduced from outside in the form of a vaccine or other substance. It can initiate primary response but do not cause disease.

So naturally acquired active immunity is the type of adaptive immunity which can cause subclinical infection.