City earnings initially take a dip (5)
I believe the answer is:
bathe
'take a dip' is the definition.
(I've seen this before)
'city earnings initially' is the wordplay.
'city' becomes 'bath' (English city).
'initially' indicates taking the first letters.
The initial letter of 'earnings' is 'e'.
'bath'+'e'='BATHE'
(Other definitions for bathe that I've seen before include "go into rollers?" , "Become immersed in" , "Wash by immersion" , "Wash, soak" , "bit of swimming" .)