Bug set off a nameless illness (6,7)
I believe the answer is:
german measles
'illness' is the definition.
(German measles is an example)
'bug set off a nameless' is the wordplay.
'bug' becomes 'germ' ('germ' can be a synonym of 'bug'**).
'set off' is an anagram indicator.
'a'+'nameless'='anameless'
'anameless' with letters rearranged gives 'anmeasles'.
'germ'+'anmeasles'='GERMAN MEASLES'
(Other definitions for german measles that I've seen before include "complaint" , "Rubella" , "viral illness" .)