Half of the pupils have a dog! (3)
I believe the answer is:
pup
'a dog' is the definition.
(I know that pup is a type of dog)
'half of the pupils' is the wordplay.
'half of' indicates taking half.
'pupils' with half the letters taken is 'PUP'.
'have' is the link.
(Other definitions for pup that I've seen before include "Young of canines" , "Whelp" , "Young of various animals" , "Young seal" , "Young animal" .)