Disease sees lamb almost destroyed (7)
I believe the answer is:
measles
'disease' is the definition.
(measles is a kind of health problem)
'sees lamb almost destroyed' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'destroyed' indicates an anagram.
'sees'+'lamb'='seeslamb'
'seeslamb' with its final letter taken away is 'seeslam'.
'seeslam' anagrammed gives 'MEASLES'.
(Other definitions for measles that I've seen before include "Children's disease with red spots" , "Children's viral disease" , "Rubeola" , "An infectious fever" , "Disease suffered in childhood" .)