Old Icelandic character appearing personally, a constant irritation (5,2,3,5)
I believe the answer is:
thorn in the flesh
'old icelandic' is the definition.
I know nothing about this answer so I can't judge whether this works.
'character appearing personally a constant irritation' is the wordplay.
I cannot quite understand how this works, but
'character' could be 'thorn' (thorn is a kind of character) and 'thorn' is found within the answer.
'constant' could be 'e' (mathematics: 2.71) and 'e' is present in the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for thorn in the flesh that I've seen before include "Source of continual annoyance" , "which is irritating" .)