Second label for animal (4)
I believe the answer is:
stag
'animal' is the definition.
(stag is a kind of animal)
'second label' is the wordplay.
'second' becomes 's' (common abbreviation).
'label' becomes 'tag' ('tag' can be a synonym of 'label'**).
's'+'tag'='STAG'
'for' acts as a link.
(Other definitions for stag that I've seen before include "Investor" , "Antlered animal" , "Male beast" , "Adult male deer, often with antlers" , "Men-only" .)