Algorithms – How to check if given $ k $ vertices efficiently create a $ k $ clique in an undirected graph $ G $

To let $ G = (V, E) $ Let be an undirected graph with a set vertex $ V $ and edge set $ E $, To let $ V & # 39; = {v_1, v_2, …, v_k } $ be a subset of $ V $ where degrees of each $ v_i $ is greater than or equal to $ k $, Is there a way to check if $ V & # 39; $ is a $ k $-clique more efficient than the brute-force algorithm in $ O (k ^ 2) $? Thank you in advance.