Terribly odd love-bird (4)
I believe the answer is:
dodo
'bird' is the definition.
(dodo is a kind of bird)
'terribly odd love' is the wordplay.
'terribly' indicates an anagram.
'love' becomes 'o' (love means zero in tennis).
'odd' is an anagram of 'dod'.
'dod'+'o'='DODO'
(Other definitions for dodo that I've seen before include "Large extinct bird" , "One deeply reactionary" , "Mauritian bird no more" , "Old-fashioned person" , "bird long dead" .)