There is a growing need to upskill higher education (HE) teachers for the effective and responsible integration of generative artificial intelligence (GenAI) in their classrooms. This case study sought to address this growing need by designing and delivering a training course for educators, focusing on the use of ChatGPT as it was the most commonly used tool at the time. The professional development opportunity lasted 5 weeks and covered critical aspects of GenAI use for teaching and learning. Data collected from participants included discussion board entries, written tasks and focus groups. Findings highlight some of the common practices and concerns HE practitioners had regarding the use of GenAI in their practice. The findings also emphasise the importance of providing teachers with customised GenAI training to facilitate its effective integration in HE contexts. Finally, based on the findings of this study, we propose the TPTP Support System for Teachers, built upon four key areas: teacher training, pedagogical support, testing revamp and practice networks. This system aims to guide institutional efforts to facilitate and support educators as they integrate GenAI in HE.