Little river, the tenth causing disease (8)
I believe the answer is:
smallpox
'disease' is the definition.
(smallpox is a kind of disease)
'little river the tenth' is the wordplay.
'little' becomes 'small' ('small' can be a synonym of 'little').
'river' becomes 'po' (Po is an example).
'the tenth' becomes 'x' (Roman numeral).
'small'+'po'+'x'='SMALLPOX'
'causing' is the link.
(Other definitions for smallpox that I've seen before include "Highly contagious viral disease with fever and skin pustules that leave permanent scars" , "Viral disease, now almost eradicated by vaccination" , "Acute viral disease, technical name variola" .)