Open English Wordnet is a key resource published in OntoLex-lemon as part of the linguistic linked open data cloud. There are, however, many links missing in the resource, and in this paper, we look at how we can establish hypernymy between adjectives. We present a theoretical discussion of the hypernymy relation and how it differs for adjectives in contrast to nouns and verbs. We develop a new resource for adjective hypernymy and fine-tune large language models to predict adjective hypernymy, showing that the methodology of TaxoLLaMa can be adapted to this task.