English name, actor, regularly referring to repeat performance (6)
I believe the answer is:
encore
'repeat performance' is the definition.
(an extension or repeat of a performance)
'english name actor regularly referring to' is the wordplay.
'english' becomes 'e' (abbreviation).
'name' becomes 'n' (common abbreviation e.g. on forms).
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'referring to' becomes 're' ('re' means regarding or about).
The alternating letters of 'actor' are 'co'.
'e'+'n'+'co'+'re'='ENCORE'
(Other definitions for encore that I've seen before include "Let's hear/see it again!" , "Call for additional performance" , "Request for repeat performance" , "Play or sing it again" , "Please play some more!" .)