The High Court will finalise a replacement for Katy Gallagher, who was disqualified from the Senate over her British ties.
Union boss David Smith is expected to be confirmed as the new ACT senator following a special recount.
The High Court will hand down the decision in Brisbane on Wednesday.
Labor MPs Josh Wilson, Justine Keay, and Susan Lamb and Centre Alliance's Rebekha Sharkie resigned earlier in May, after the High Court ruled Ms Gallagher was ineligible to stay in parliament.
The date for those lower house by-elections and a fifth one sparked by Tim Hammond's decision to quit for family reasons, is yet to be named.