The Dragons jet Down Under for a three-Test series with the Lions' next opponents on the back of a World Cup semi-final and Six Nations Grand Slam.
Wales have not tasted victory over the Wallabies since the 21-18 Millennium Stadium victory in 2008, and Priestland is more than aware of the mounting expectation for a major scalp.
"There is added pressure now because every time we go on the field, people expect us to win," said Priestland.
"The nation wants a southern hemisphere scalp as well and, hopefully, we can get one before the autumn."
The Wallabies claimed two slender victories over Wales last year. First in the World Cup Bronze Final and then in Shane Williams' farewell at the Millennium Stadium.
Priestland insists the familiarity between the two sides will play into Wales' hands and reckons the Grand Slam champions can take advantage of injuries in the Australia camp.
"We know what to expect because they have world class players and some of the most skilful players in world rugby," added the fly-half.
"Any time you play against them, you have to be at your best otherwise they will cut you to pieces.
"We have an opportunity going down there, it will be tough. They have a few injuries and we have a few injuries so it's a good time to play them.
"You have to be at your best and hopefully we prepare well and give ourselves the best possible chance to get a southern hemisphere scalp."
Wales face Australia on June, 9, 16 and 23, and also face Super 15 outfit ACT Brumbies in a mid-week fixture.