according to the Stirling council website, as below
The Coat of Arms is decorated with two caltrops (iron spikes) and two rowels(spiked wheels on a horse’s spurs), representing the Battle of Bannockburn in1314.
The Scottish Lion Rampant on the shield indicates the former close association of the Royal Stewarts with the Stirling area.The supporters are a goshawk, representing the Drummonds, who were for centuries the principal family of southern Perthshire and were founders of Callander in1739, and a wolf, representing the former Royal Burgh of Stirling. The wolf comes from the 9th century legend when a howling wolf saved the town from a Viking attack.
In December 2011 – it was decided that a motto would be added to the coat of arms:Steadfast as the Rock
Like their Castle perched on a rock, the people of the Stirling area have stood proud and steadfast through the ages. Rock solid, loyal and resolute - like so many characters from our past,and like the troops who have fought for freedom all over the world over the years from their Castle home."