A kid born in Caen out by the sea? (9)
I believe the answer is:
caribbean
'the sea?' is the definition.
(Caribbean is an example)
'a kid born in caen out' is the wordplay.
'kid' becomes 'rib' (I've seen this before**).
'born' becomes 'b'.
'in' is an insertion indicator.
'out' means one lot of letters goes inside another.
'rib'+'b'='ribb'
'ribb' inserted into 'caen' is 'caribben'.
'a' inserted inside 'caribben' is 'CARIBBEAN'.
'by' acts as a link.
(Other definitions for caribbean that I've seen before include "Sea south of the US" , "Sea between North and South America" , "who lives on an island?" , "West Indies sea" , "WI" .)