As of January 2025[update] he is chair of the Independent Health and Aged Care Pricing Authority and of the Stretton Institute at the University of Adelaide.
[4] While secretary of that department in 2013, Tune was forced to sign off controversial tax-funded advertising intended to deter asylum seekers from making the journey to Australia by boat, during the care-taker period before an election.
Penny Wong, leader of the Senate for the Labor Party, who had worked with him during her stint as finance minister, said "His sustained contribution to public policy making has been profound".
[11] In the review, Tune and his colleague John Conde proposed a new "principles-based" system and recommended the language of "entitlements" be renamed "work expenses".
This review looked at the workings of the National Archives of Australia (NAA), which had been criticised for taking a long time to deliver information, which was largely due to waiting for advice from other agencies, in particular sensitive records and those related to national security, before it is able to decide whether to declassify records and release them.
Another issue is the deterioration of many records in storage, leading to potential be breaches of Part 5 Section 24 of the Public Governance, Performance and Accountability Act 2013.
[19][20] In October 2022, Tune was appointed to lead the Independent Capability Review of the Aged Care Quality and Safety Commission.
This body "provides independent and transparent advice to the Australian Government in relation to funding for public hospitals and residential aged care services".