Animal has no time for teacher (5)
I believe the answer is:
rabbi
'teacher' is the definition.
(Jewish teacher)
'animal has no time for' is the wordplay.
'animal' becomes 'rabbit' (I've seen this before).
'has no' suggests deleting specific letters.
'time for' becomes 't' (I've seen this in other clues).
'rabbit' with 't' taken out is 'RABBI'.
(Other definitions for rabbi that I've seen before include "Spiritual leader of a Jewish congregation" , "Sacks, for example" , "Teacher of Jewish law" , "Religious scholar" , "Religious leader in a Jewish community" .)