Not one increase could be genuine (7)
I believe the answer is:
sincere
'genuine' is the definition.
('sincere' can be a synonym of 'genuine')
'not one increase could be' is the wordplay.
'not' indicates named letters should be taken away.
'one' becomes 'a'.
'could be' is an anagram indicator.
'increase' with 'a' taken out is 'increse'.
'increse' with letters rearranged gives 'SINCERE'.
(Other definitions for sincere that I've seen before include "like informal correspondents?" , "(Of person) genuine" , "Open and genuine, not deceitful" , "Earnest" , "Unaffected" .)