Terrible puns -- air's becoming sort of blue (8)
I believe the answer is:
prussian
'sort of blue' is the definition.
'terrible puns air's' is the wordplay.
'terrible' indicates anagramming the letters.
'puns'+'airs'='punsairs'
'punsairs' is an anagram of 'PRUSSIAN'.
'becoming' is the link.
(Other definitions for prussian that I've seen before include "Relating to a former German state" , "Ova" , "Native of a former German kingdom" .)