Brynner Theatre's closing for the festive season (4)
I believe the answer is:
yule
'the festive season' is the definition.
'brynner theatre's closing' is the wordplay.
'brynner' becomes 'yul' (Yul Brynner).
'closing' indicates one should take the final letters (the letter which ends or closes the word).
The last letter of 'theatre' is 'e'.
'yul'+'e'='YULE'
'for' is the link.
(Other definitions for yule that I've seen before include "Christmas period" , "festive tide" , "Christmas-time" , "Christmas season" , "Noel" .)