Cornish region perhaps welcoming to store? (4)
I believe the answer is:
stow
'store?' is the definition.
('stow' can be a synonym of 'store')
'cornish region perhaps welcoming to' is the wordplay.
'cornish region perhaps' becomes 'SW' (South West of England).
'welcoming' indicates putting letters inside (in sense of 'inviting in').
'sw' going around 'to' is 'STOW'.
(Other definitions for stow that I've seen before include "Pack or store carefully, luggage perhaps" , "Pack (in proper place)" , "Keep under hatches" , "Lay up, pack away" , "Fill by packing tightly" .)