I'm annoyed by wet weather in sheikhdom (7)
I believe the answer is:
bahrain
'sheikhdom' is the definition.
(I've seen this before)
'i'm annoyed by wet weather' is the wordplay.
'i'm annoyed' becomes 'bah' (I can't justify this - if you can you should give a lot more credence to this answer).
'by' says to put letters next to each other.
'wet weather' becomes 'rain' (rain is wet weather).
'bah'+'rain'='BAHRAIN'
'in' is the link.
Can you help me to learn more?
(Other definitions for bahrain that I've seen before include "Gulf region?" , "Arab sheikhdom" , "Arab state" , "kingdom in Middle East" , "Island country in the Persian Gulf" .)