Call up Greek character over issue (7)
I believe the answer is:
emanate
'issue' is the definition.
(both can mean to give out or radiate)
'call up greek character over' is the wordplay.
'call' becomes 'name' (synonyms).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'greek character' becomes 'eta' (letter from the Greek alphabet).
'over' shows that the letters should be reversed in order.
'name' reversed gives 'eman'.
'eta' backwards is 'ate'.
'eman'+'ate'='EMANATE'
(Other definitions for emanate that I've seen before include "Issue or spread out from a source" , "Proceed or issue forth" , "Send out" , "Manatee (anag.)" , "Come out (of source)" .)