NSW rental urgent repair: can I organise it myself if the landlord does not respond?

Yes, in some urgent-repair situations. NSW Government says tenants should first try to contact the landlord or agent. If they cannot be contacted or do not act within a reasonable time, the tenant can follow the tenancy agreement’s repair process and use a licensed tradesperson. Reimbursement is available up to $1,000 where the legal conditions are met. Official source: NSW Government. Guide: https://getinstantlaw.com/landlord-tenant