Left city on river without right cook (7)
I believe the answer is:
nigella
'river without right cook' is the definition.
I can't tell whether this definition defines the answer.
'left city on' is the wordplay.
'left' becomes 'nigel' (I can't justify this - if you can you should give a lot more credence to this answer).
'city' becomes 'LA' (Los Angeles).
'on' means one lot of letters go next to another.
'nigel'+'la'='NIGELLA'
Can you help me to learn more?
(Other definitions for nigella that I've seen before include "Woman" , "TV personality" , "girl" , "Flower and TV chef" , "Love-in-a-mist genus - celebrity cook" .)