Identify the one who was not a ‘New Critic’:

The correct option is Claude Levi-Strauss.

New Criticism was a formalist movement in literary theory that dominated American literary criticism in the middle decades of the 20th century. It emphasized close reading, particularly of poetry, to discover how a work of literature functioned as a self-contained, self-referential aesthetic object.

Let us look at the figures mentioned in the options to understand why Claude Levi-Strauss is the correct answer:
1. Allen Tate, Robert Penn Warren, and Cleanth Brooks were all prominent American literary critics, poets, and members of the Southern Agrarians who became foundational figures of the New Criticism movement. In fact, Cleanth Brooks and Robert Penn Warren co-authored the highly influential textbooks Understanding Poetry (1938) and Understanding Fiction (1943), which helped institutionalize New Critical methods in American universities.
2. Claude Levi-Strauss, on the other hand, was a French anthropologist and ethnologist. He is widely regarded as the founder of structural anthropology and a key figure in the development of structuralism, which is a completely different theoretical framework from New Criticism.

Therefore, Claude Levi-Strauss is the only figure listed who was not a 'New Critic'.