At home, permitted to see bay (5)
I believe the answer is:
'bay' is the definition.
(I've seen this before)
'at home permitted' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'permitted' becomes 'let' (to let something happen is to permit it).
'to see' acts as a link.
(Other definitions for inlet that I've seen before include "Opening - passage" , "Fiord" , "Opening through which fluid can pass" , "Small arm of the sea" , "Gulf" .)