Islander's language makes person cross (4)
I believe the answer is:
manx
'islander's language' is the definition.
'Manx' can be an answer for 'language' (Manx is an example). I am not certain of the 'islander's' bit.
'person cross' is the wordplay.
'person' becomes 'man' (man is a kind of person).
'cross' becomes 'x' (an X is a cross).
'man'+'x'='MANX'
'makes' is the link.
Can you help me to learn more?
(Other definitions for manx that I've seen before include "Type of cat, of shearwater" , "Breed of tailless cat" , "Adjective indicating the Isle of Man" , "The natives' language" , "To do with the Isle of Man - say a cat" .)