Feel Berlin is home to ... not this river (4)
I believe the answer is:
elbe
'not this river' is the definition.
'elbe' can be an answer for 'river' (I have seen 'River of Germany ' mean 'elbe' so perhaps 'river' could also mean 'elbe'). I'm unsure of the remainder of the definition.
'feel berlin is home to' is the wordplay.
'is home to' indicates a hidden word (part of the clue is home to the answer).
'ELBE' is hidden in the letters of 'feel berlin'.
(Other definitions for elbe that I've seen before include "River of Germany" , "German banker" , "It flows through Germany" , "Flower" , "Dresden and Hamburg's river" .)