First aid by guest eliminates saint's fever (4)
I believe the answer is:
ague
'fever' is the definition.
(I've seen this in another clue)
'first aid by guest eliminates saint's' is the wordplay.
'first aid' becomes 'a' (1st letter of 'aid').
'by' means one lot of letters go next to another.
'eliminates' suggests deleting specific letters.
'saint' becomes 'st' (abbreviation).
'guest' with 'st' removed is 'gue'.
'a'+'gue'='AGUE'
(Other definitions for ague that I've seen before include "Fit of the shakes" , "Fever with shivers" , "Fit of shivering and shaking" , "attack" , "Feverish fit" .)