If an office holder with Tier 2 travel entitlements is flying between Sydney, Melbourne or Canberra as one leg of a multi-leg trip, must that leg of the journey be at economy class?

No. If an office holder with Tier 2 travel entitlements has a flight between Sydney, Melbourne or Canberra as a leg of a multi-leg trip where another leg is at business class, the office holder is entitled to travel for the whole trip at business class. For example, if an office holder is travelling from Darwin to Canberra, with a stopover in Sydney, they are entitled to travel at business class for both legs.