Probably not much at all. If you think any interest rates are important to the price of gold (I don't!), keep you eye on US rates. That is where the real game is.
Note: Readers may have noticed that the four major Australian banks have increased rates on mortgage lending. Some have called it profit gauging, and others have taken it the anticipation of increases in the cash rate. Neither is true.
The RBA and APRA have been concerned about inflated housing prices for some time. (Since 2001 in my direct experience.) They are worried about what a rapid deflation of Australian house prices might do to the financial stability of the Australian banks. It looks like they have finally done something that I had suggested elsewhere six years ago, and increased the capital requirement mortgage loans. The banks have been forced to raise more capital, which has a cost. That cost has to be recovered by a price increase, and the RBA and APRA get what they want - a targeted increase in interest rates that impacts the sector they are worried about, while leaving others unaffected.
Is this relevant to the price of gold. I don't think so, but for those who seriously think that systemic banking collapse is possible and that buying overprice gold coins and ingots is a reasonable response, this example of good financial regulation is probably bad news.