Greek character and daughter, for example, brought up reminder (5)
I believe the answer is:
nudge
'reminder' is the definition.
(I've seen this before)
'greek character and daughter for example brought up' is the wordplay.
'greek character' becomes 'nu' (Greek letter).
'and' says to put letters next to each other.
'daughter' becomes 'd' (genealogical abbreviation).
'for example' becomes 'e.g.' (short for 'exempli gratia', 'for example' in Latin).
'brought up' shows that the letters should be reversed in order (in a down clue, letters go up).
'eg' back-to-front is 'ge'.
'nu'+'d'+'ge'='NUDGE'
(Other definitions for nudge that I've seen before include "Gentle encouragement" , "suggestive move" , "A gentle reminder?" , "Poke gently with elbow" , "Prod gently with elbow" .)