Monster is half frog, half hare (4)
I believe the answer is:
ogre
'monster' is the definition.
(fairy tale monster)
'half frog half hare' is the wordplay.
'half' indicates taking half.
'half' means to take half the letters.
'frog' with half the letters taken is 'og'.
'hare' cut in half is 're'.
'og'+'re'='OGRE'
'is' acts as a link.
(Other definitions for ogre that I've seen before include "Fairy tale monster" , "Human-eating giant" , "Wicked and inhuman person" , "Terrifying man" , "One to gobble flesh" .)