Encourage trendy quote (6)
I believe the answer is:
incite
'encourage' is the definition.
(I've seen this before)
'trendy quote' is the wordplay.
'trendy' becomes 'in' ('in' can mean fashionable).
'quote' becomes 'cite' (synonyms).
'in'+'cite'='INCITE'
(Other definitions for incite that I've seen before include "drive" , "Whip up" , "Egg on" , "Stir up (eg, violence)" , "Urge, instigate" .)