A very common workflow is to index some data based on its embeddings and then given a new query embedding retrieve the most similar examples with k-Nearest Neighbor search. For example, you can imagine embedding a large collection of papers by their abstracts and then given a new paper of interest retrieve the most similar papers to it.
TLDR in my experience it ~always works better to use an SVM instead of kNN, if you can afford the slight computational hit
S. Kiritchenko, X. Zhu, C. Cherry, and S. Mohammad. Proceedings of the 8th International Workshop on Semantic Evaluation (SemEval 2014), page 437--442. Dublin, Ireland, Association for Computational Linguistics, (August 2014)
P. Molchanov, S. Gupta, K. Kim, and J. Kautz. The IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, page 1-7. IEEE, (September 2015)