In this paper, we present a domain-independent ontology extension workflow supported by LLMs. Ontology Engineering (OE) is a complex field that requires combining technical skills with domain expertise across multiple disciplines. Despite numerous attempts at automation, most of the processes are still manual. Different ontology engineering methodologies coexist, but none is a standard. These challenges, together with the lack of highly skilled workers in the sector, increase the entry barriers to the field. In parallel, Large Language Models (LLMs) are becoming prominent in ontology development due to their natural language processing and coding capabilities and their reportedly emergent abilities. In this paper, we focus on human-LLM collaboration for ontology extension. Following a Design Science Research approach, we interviewed 11 experts and modeled the current process of ontology extension to disclose its main issues. We analyzed the concerns and opportunities perceived by ontology engineers for using LLMs. Based on our insights and previous work, we designed a process framework for ontology extension that combines human expertise with LLMs capabilities, providing customizable prompt templates, OE tools, and guidelines. We tested our methodology with an existing greenhouse ontology using GPT-4o. Finally, we qualitatively evaluated the results against a manually crafted extension we use as our gold standard. The results show that the proposed approach holds the potential to (1) get inspiration for adding new entities, (2) deal with complex syntax definitions and repetitive tasks, and (3) verify whether the extended ontology conforms to the requirements and competency questions.