Cover for the Times entertaining the City (7)
I believe the answer is:
protect
'cover' is the definition.
(I know that cover is a more specific form of the action protect)
'for the times entertaining the city' is the wordplay.
'for' becomes 'pro' (as in being 'pro' something).
'the times' becomes 'tt' (an abbreviation for time written twice).
'entertaining' means one lot of letters goes inside another (inviting in, as for dinner).
'the city' becomes 'EC' (the City of London postcode).
'tt' going around 'ec' is 'tect'.
'pro'+'tect'='PROTECT'
(Other definitions for protect that I've seen before include "Guard" , "Keep safe" , "Keep from danger" , "Take care of" , "Safeguard" .)