John Foley took early retirement from the organisation last year, receiving a controversial £57,000 golden handshake.
The Scotsman understands he has been served with a witness order, meaning he must attend the tribunal or risk committing a criminal offence.
The SPA, which was set up to manage the £1.1 billion police budget and hold the chief constable to account, last year endured months of criticism over its performance, leading to the departure of Mr Foley and the chair of its board, Andrew Flangan.
After his departure, it emerged Mr Foley had received a £57,000 golden handshake payment on top of an early retirement payment of £43,470.
The ongoing employment tribunal, which resumes on Monday, has heard claims that during Mr Foley’s time in charge, a senior executive at the SPA received a £165,000 payoff weeks after being arrested for domestic abuse.
Whistleblower Amy McDonald has also told the tribunal that former Deputy Chief Constable Rose Fitzpatrick asked for taxpayer-funded relocation expenses to be paid by cash transfer.
Asked to comment on Mr Foley, a spokeswoman for the SPA said: “It would be inappropriate to comment on this specific case while legal proceedings are ongoing.”