Actor gives reading at new production (9)
I believe the answer is:
tragedian
'actor' is the definition.
(tragedian is a kind of actor)
'reading at new production' is the wordplay.
'new production' is an anagram indicator.
'reading'+'at'='readingat'
'readingat' with letters rearranged gives 'TRAGEDIAN'.
'gives' acts as a link.
(Other definitions for tragedian that I've seen before include "Serious actor" , "Egad, I rant about actor in sad drama" , "Dramatist" , "A great din (anag) - actor" , "actor in Macbeth?" .)