A zebra harmed on New Year’s Day for country (10)
I believe the answer is:
azerbaijan
'country' is the definition.
(I've seen this before)
'a zebra harmed on new year's day' is the wordplay.
'harmed' indicates anagramming the letters.
'on' indicates putting letters inside (as in clothing \'on\' a person).
'new year's day' becomes 'ijan' (resembles 1 Jan - 1st January is New Year's Day).
'zebra' with letters rearranged gives 'zerba'.
'a' placed into 'zerba' is 'azerba'.
'azerba'+'ijan'='AZERBAIJAN'
'for' acts as a link.
(Other definitions for azerbaijan that I've seen before include "Baku's country" , "in Asia" , "republic" , "Country in the South Caucasus" .)