He is getting irritated with nun's bright outlook (8)
I believe the answer is:
sunshine
'bright outlook' is the definition.
(sunshine is bright weather)
'he is getting irritated with nun's' is the wordplay.
'getting' says to put letters next to each other.
'irritated with' indicates an anagram (I've seen this in other clues).
'he'+'is'='heis'
'heis' with its letters anagrammed with 'nuns' can make 'SUNSHINE'.
(Other definitions for sunshine that I've seen before include "Brightness" , "that appears at dawn" , "Daily light and warmth" , "term of address" , "Light, cheerfulness" .)