In an age of surveillance capitalism, anchoring the design of emerging smart services in trustworthiness is urgent and important. Edge Intelligence, which brings together the fields of AI and Edge computing, is a key enabling technology for smart services. Trustworthy Edge Intelligence should thus be a priority research concern. However, determining what makes Edge Intelligence trustworthy is not straight forward. This paper examines requirements for trustworthy Edge Intelligence in a concrete application scenario of voice-activated services. We contribute to deepening the understanding of trustworthiness in the emerging Edge Intelligence domain in three ways: firstly, we propose a unified framing for trustworthy Edge Intelligence that jointly considers trustworthiness attributes of AI and the IoT. Secondly, we present research outputs of a tangible case study in voice-activated services that demonstrates interdependencies between three important trustworthiness attributes: privacy, security and fairness. Thirdly, based on the empirical and analytical findings, we highlight challenges and open questions that present important future research areas for trustworthy Edge Intelligence.