The Brisbane District Court heard that McMullen, 49, dishonestly helped recruit Stamp's daughter to an unnecessary role in design and media services for $80,000 a year, when many staff were being laid off because of major cuts to the public health service.
"Stamp has a bombastic personality, he was an arrogant man who did exert power on those below him, including Mr McMullen," Crown Prosecutor Dzenita Balic said.
Australian taxpayers forked out $26,000 before the nepotism was uncovered.
The court heard Stamp received the benefit of having his daughter employed and able to stay in Australia on a working visa, the Courier Mail reported.
When the conduct was revealed, he put pressure on McMullen to "make it disappear", the Courier Mail reported.
McMullen pleaded guilty to two counts of receiving secret commissions and was given a two-year suspended jail term.
Stamp is believed to be back in the United Kingdom and the warrant for his arrest would not be activated unless he returned to Australia.
The warrant was issued after a three-year investigation into the corruption at Metro North Hospital and Health Service.
Stamp received a CBE for his services to healthcare in 2002 and had 18 years' experience as a chief executive in the British National Health Service when he came to New Zealand in 2006.
At the time, his daughter worked as a graphic designer at Waikato Business Publications.
No allegation of misconduct was made against Katy Stamp during the Australian investigation.
Stamp, now 66, was less than a year into his role at Waikato DHB when he left.