Wind that's extremely lively after festival (8)
I believe the answer is:
easterly
'wind' is the definition.
(easterly is a kind of wind)
'extremely lively after festival' is the wordplay.
'extremely' says to hollow out the word (remove centre letters).
'after' says to put letters next to each other.
'festival' becomes 'easter' (I've seen this before**).
'lively' with its centre removed is 'ly'.
'ly' put after 'easter' is 'EASTERLY'.
'that's' acts as a link.
(Other definitions for easterly that I've seen before include "Year's let (anag) - direction of 15" , "Of wind, blowing from direction of rising sun" , "The sort of wind that brings cold air to this country" , "Invariably cold wind" , "large blow" .)