It finishes fast, getting new direction (7)
I believe the answer is:
eastern
'direction' is the definition.
(I've seen this before)
'it finishes fast getting new' is the wordplay.
'it finishes fast' becomes 'Easter' (the fast of Lent ends at Easter).
'getting' means one lot of letters go next to another.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'easter'+'n'='EASTERN'
(Other definitions for eastern that I've seen before include "China?" , "Could be Chinese" , "in Beijing, possibly" , "See 11" , "Facing away from the west" .)