Is annoyed by alien’s way of thinking (7)
I believe the answer is:
mindset
'way of thinking' is the definition.
(I've seen this before)
'is annoyed by alien's' is the wordplay.
'is annoyed by' becomes 'minds' (to mind something can mean to be bothered by it).
'alien' becomes 'et' (extra terrestrial).
'minds'+'et'='MINDSET'
(Other definitions for mindset that I've seen before include "thinking normally" , "way of thinking" , "fixed attitude" , "Outlook" , "convictions" .)