Burns's birthplace (3)
I believe the answer is:
'burns's birthplace' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for ayr that I've seen before include "Scottish resort" , "Scottish town sounds tuneful" , "Scots. town; sounds like song" , "Town in Strathclyde" , "Town on Firth of Clyde" .)