Found time to get flu badly — careless! (9)
I believe the answer is:
forgetful
'careless' is the definition.
(thesaurus)
'found time to get flu badly' is the wordplay.
'found' becomes 'forge' (I've seen this in other clues).
'time' becomes 't' (abbreviation).
'to get' means one lot of letters goes inside another.
'badly' indicates anagramming the letters (letters in the wrong order).
'flu' anagrammed gives 'ful'.
't' inserted within 'ful' is 'tful'.
'forge'+'tful'='FORGETFUL'
(Other definitions for forgetful that I've seen before include "Apt not to remember" , "Distracted" , "Inclined not to remember" , "Absent-minded" , "Not remembering" .)