Take charge of narrative, lifting a veil (6)
I believe the answer is:
mantle
'a veil' is the definition.
(thesaurus)
'take charge of narrative lifting' is the wordplay.
'take charge of' becomes 'man' (man can mean to control or be in charge of).
'narrative' becomes 'elt' (I am not sure about this - if you are sure you should believe this answer much more).
'lifting' is a reversal indicator.
'elt' written backwards gives 'tle'.
'man'+'tle'='MANTLE'
(Other definitions for mantle that I've seen before include "Goes over light" , "A cloak, cover" , "Robe or gas-lamp fitting" , "Loose outer garment or covering" , "Layer below earth's crust" .)