Say Arab and American will show narcissism (8)
I believe the answer is:
egomania
'show narcissism' is the definition.
'egomania' can be an answer for 'narcissism' (I've seen this in another clue). I'm unsure of the 'show' bit.
'say arab and american' is the wordplay.
'say' becomes 'eg' (both can mean for example).
'arab' becomes 'Omani' (someone from Oman).
'and' says to put letters next to each other.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'eg'+'omani'+'a'='EGOMANIA'
'will' acts as a link.
Can you help me to learn more?
(Other definitions for egomania that I've seen before include "Excessive or irrational self-conceit" , "Self-obsession" , "Feeling very self-conscious" , "Obsessive self-interest" , "selfish obsession" .)