Refuse to let one in, which shows intelligence (5)
I believe the answer is:
brain
'shows intelligence' is the definition.
'brain' can be an answer for 'intelligence' (brain is a kind of intelligence). I'm unsure of the 'shows' bit.
'refuse to let one in' is the wordplay.
'refuse' becomes 'bran' (I've seen this before).
'to let one' becomes 'i' (I am not sure about this - if you are sure you should believe this answer much more).
'in' means one lot of letters goes inside another.
'bran' placed around 'i' is 'BRAIN'.
'which' is the link.
Can you help me to learn more?
(Other definitions for brain that I've seen before include "Intelligent person" , "Mind" , "Thinking thing" , "Organ of the intellect" , "to get hit over the head" .)