The rapid integration of generative AI (GenAI) tools into higher education (HE) presents both transformative opportunities and pressing challenges, particularly in English-medium education (EME) classrooms. While GenAI tools offer innovative possibilities for enhancing instruction, assessment, and learner autonomy, they also raise concerns about the erosion of meaningful language and content learning experiences through over-automation and excessive reliance on algorithmic output without involving students' thinking process. This Element offers a timely, practitioner-focused exploration of how GenAI tools can be thoughtfully integrated into both language and content-subject teaching while addressing key threats GenAI poses within EME contexts. The Element does not seek to promote the uncritical adoption of GenAI into HE but instead offers a pragmatic way forward that recognises the essential role of agentic teachers in supporting student content and language learning.