High point after New Year's Day for one cleaning up (7)
I believe the answer is:
janitor
'one cleaning up' is the definition.
(a janitor cleans a building)
'high point after new year's day' is the wordplay.
'high point' becomes 'tor' (a tor is a rocky hill).
'after' says to put letters next to each other.
'new year's day' becomes 'JANI' (resembles Jan 1st).
'tor' put after 'jani' is 'JANITOR'.
'for' acts as a link.
(Other definitions for janitor that I've seen before include "Caretaker or doorkeeper" , "One employed to clean and maintain a building" , "Person looking after building" , "(In Scotland) school caretaker" , "Caretaker (mainly US)" .)