Queen leaves festival in this direction (4)
I believe the answer is:
east
'this direction' is the definition.
(compass direction)
'queen leaves festival' is the wordplay.
'queen' becomes 'ER' (abbreviation for Elizabeth Regina).
'leaves' is a deletion indicator.
'festival' becomes 'Easter' (Christian festival).
'easter' with 'er' taken out is 'EAST'.
'in' acts as a link.
(Other definitions for east that I've seen before include "4 dn 17 dn" , "Compass point at 90 degrees" , "Opposite of west" , "Compass direction" , "Asia" .)