Teacher and student finally chatter (6)
I believe the answer is:
rabbit
'chatter' is the definition.
(both can mean to talk excessively)
'teacher and student finally' is the wordplay.
'teacher' becomes 'rabbi' (Jewish teacher).
'and' means one lot of letters go next to another.
'finally' says to take the final letters.
The final letter of 'student' is 't'.
'rabbi'+'t'='RABBIT'
(Other definitions for rabbit that I've seen before include "Gas" , "Burrowing creature" , "Furry rodent" , "may be pulled out of Derby, perhaps" , "Come up with a solution and pull one out of the hat" .)