'Daily Chronicle', initially thinner (7)
I believe the answer is:
cleaner
'daily' is the definition.
(dated term for a woman cleaner)
'chronicle initially thinner' is the wordplay.
'initially' says to take the initial letters.
'thinner' becomes 'leaner' ('lean' can be a synonym of 'thin').
The first letter of 'chronicle' is 'c'.
'c'+'leaner'='CLEANER'
(Other definitions for cleaner that I've seen before include "less sleazy?" , "Eg, launderer, duster" , "Char, daily" , "More sanitary" , "Maybe Daily" .)