Worry about being taken in by daily (4)
I believe the answer is:
fret
'worry' is the definition.
(to fret about something is to worry)
'about being taken in by daily' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'being taken in by' is an insertion indicator.
'daily' becomes 'FT' (Financial Times, daily newspaper).
're' put inside 'ft' is 'FRET'.
(Other definitions for fret that I've seen before include "Worry; wet mist" , "Worry or agitate" , "Wear away" , "Vex oneself - part of a fingerboard" , "Anguish" .)