Faint hint of narcissism displayed in Syco: training is required (7)
I believe the answer is:
syncope
'faint' is the definition.
('syncope' can be a synonym of 'faint')
'hint of narcissism displayed in syco training is required' is the wordplay.
'hint of' indicates taking the first letters.
'displayed in' indicates putting letters inside.
'training' becomes 'pe'.
'is required' means one lot of letters go next to another.
The initial letter of 'narcissism' is 'n'.
'n' put inside 'syco' is 'synco'.
'synco'+'pe'='SYNCOPE'
(Other definitions for syncope that I've seen before include "Omission of sounds or letters in middle of word" , "Temporary consciousness loss; spy once (anag.)" .)