League ignoring the French complaint (4)
I believe the answer is:
ague
'complaint' is the definition.
(ague is a kind of disease)
'league ignoring the french' is the wordplay.
'ignoring' is a deletion indicator.
'the french' becomes 'le' ('the' in French).
'league' with 'le' taken away is 'AGUE'.
(Other definitions for ague that I've seen before include "Hot and cold fever" , "Fit of shivering and shaking" , "Sickness" , "Acute fever; shivering fit" , "Chills and fever" .)