Odd about duck being an extinct species (4)
I believe the answer is:
dodo
'an extinct species' is the definition.
(I know that dodo is a extinct species)
'odd about duck' is the wordplay.
'about' indicates an anagram.
'duck' becomes 'o' (resembles zero - 'duck' in cricket).
'odd' anagrammed gives 'dod'.
'dod'+'o'='DODO'
'being' acts as a link.
(Other definitions for dodo that I've seen before include "Extinct bird of Mauritius, very dead" , "Two rooks - one was unable to fly" , "E [EXTINCT] bird" , "Square" , "Mauritian bird no more" .)