Shut up home in the immediate vicinity (5,8)
I believe the answer is:
close quarters
'in the immediate vicinity' is the definition.
I can't judge whether this definition defines the answer.
'shut up home' is the wordplay.
'shut' becomes 'close' (synonyms).
'up home' becomes 'quarters' (I can't justify this - if you can you should give a lot more credence to this answer).
'close'+'quarters'='CLOSE QUARTERS'
Can you help me to learn more?
(Other definitions for close quarters that I've seen before include "nearly in battle" , "at a very short distance" , "Accommodation for canons" .)