Sensitive about the first shop (5)
I believe the answer is:
store
'shop' is the definition.
(I know that shop can be written as store)
'sensitive about the' is the wordplay.
'sensitive' becomes 'sore' (as in a sore wound).
'about' means one lot of letters goes inside another.
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'sore' going around 't' is 'STORE'.
'first' is the link.
(Other definitions for store that I've seen before include "Put by; shop" , "Put away for future use" , "Stock or supply, or warehouse for them" , "Save" , "Shop; repository" .)