See alms distributed for illness (7)
I believe the answer is:
measles
'for illness' is the definition.
(measles is a kind of illness)
'see alms distributed' is the wordplay.
'distributed' indicates anagramming the letters.
'see'+'alms'='seealms'
'seealms' anagrammed gives 'MEASLES'.
(Other definitions for measles that I've seen before include "Rubeola" , "Children's viral disease" , "Morbilli is technical term for this illness" , "Disease suffered in childhood" , "Disease where spots may be seen" .)