The court is likely to refer it to the arbitrator to decide
Australia's laws follow the model UN codes as do most jurisdictions so this should be pretty universal.
There are two basic principles going to jurisdiction in an arbitration agreement: the severability principle and the competence-competence principle.
The severability principle is that an arbitration agreement is a separate (severable) contract from any other agreement between the parties even if they are in the same document. So, the fact that the contract has expired, or is even void, is irrelevant - the arbitration agreement stands or falls on its own. For the arbitration agreement to have expired, the expiration clause would need to be explicit that it includes the arbitration clause.
The competence-competence principle is that the arbitrator has the authority (competence 1) to decide if they are allowed to be the arbitrator (competence 2). So, at first instance, it is the job of the arbitrator to decide whether there is or isn't a valid arbitration agreement and, therefore, whether they can continue with the arbitration. The parties are allowed to make submissions on this but only until the statement of defence is submitted. A decision by an arbitrator that they do have jurisdiction is one of the few things that a court can review, but only if referred to the court within 30 days.
Therefore, unless the arbitration agreement is unenforcable on its face, the court will tell the parties to follow it.