A chef initially varied menu, showing insight (6)
I believe the answer is:
acumen
'insight' is the definition.
(I've seen this before)
'a chef initially varied menu' is the wordplay.
'initially' suggests taking the first letters.
'varied' is an anagram indicator.
The initial letter of 'chef' is 'c'.
'menu' is an anagram of 'umen'.
'a'+'c'+'umen'='ACUMEN'
'showing' is the link.
(Other definitions for acumen that I've seen before include "Wit" , "intuition" , "Quick intelligence" , "The ability to make good and quick decisions" , "Being sharp" .)