Where teacher's pet is? That’s close to bull! (4,4)
I believe the answer is:
near miss
This clue could be a double definition.
'where teacher's pet is?' is the first definition.
The definition suggests a singular noun which matches the answer.
'that's close to bull' is the second definition.
(shot close to a bullseye)
(Other definitions for near miss that I've seen before include "not a success" , "meeting thankfully avoided" , "Close thing" , "narrowly averted disaster" , "girl next door" .)