Find out by being elected into one of the HSG`s committees.
Committee work on top of everything else? Academic self-governance is time-consuming. Yet being involved in it also gives you access to insider knowledge on the workings of an academic institution and the micro-political constellations with it, and provides you with first-hand information that is relevant to your day-to-day life as an academic. Knowing how individuals or project proposals are assessed will come in useful when you start applying for research funding. Knowing issues that are being discussed in the Senate or your School can help you align your strategy accordingly. Last but not least, through committee work you will be able to establish contacts with representatives of other academic institutions.
Find out from your contact person among the non-tenured faculty which committee seats are to be filled and mention that you would like to represent the non-tenured faculty during an appointments process.