Leaving old city, fever becomes mild (9)
I believe the answer is:
temperate
'mild' is the definition.
('temperate' can be similar in meaning to 'mild')
'leaving old city fever' is the wordplay.
'leaving' is a deletion indicator.
'old city' becomes 'ur' (ancient city state).
'fever' becomes 'temperature'.
'temperature' with 'ur' taken away is 'TEMPERATE'.
'becomes' acts as a link.
(Other definitions for temperate that I've seen before include "Restrained" , "Calm" , "Abstemious" , "It is reasonable" , "sober" .)