Rancour in a north-east Texas city (7)
I believe the answer is:
abilene
'texas city' is the definition.
(I've seen this in another clue)
'rancour in a north-east' is the wordplay.
'rancour' becomes 'bile' (I can't explain this - if you can you should give a lot more credence to this answer).
'in' is an insertion indicator.
'north east' becomes 'ne'.
'a'+'ne'='ane'
'bile' inserted inside 'ane' is 'ABILENE'.
Can you help me to learn more?
(Other definitions for abilene that I've seen before include "US city" , "Kansas City?" , "Texan city" , "Texas city" .)