Adding a dash of PR puff about hot country (11)
I believe the answer is:
hyphenation
'adding a dash' is the definition.
'pr puff about hot country' is the wordplay.
'pr puff' becomes 'hype'.
'about' is an insertion indicator.
'hot' becomes 'h'.
'country' becomes 'nation' ('nation' can be a synonym of 'country').
'hype' going around 'h' is 'hyphe'.
'hyphe'+'nation'='HYPHENATION'
'of' acts as a link.
(Other definitions for hyphenation that I've seen before include "Act of joining with a dash" , "Dashing through manuscripts" .)