This is a hidden word puzzle - the answer is literally hidden within consecutive letters of other words in the clue.
Look for the answer spelled out in consecutive letters across the words 'dispatching zebras'. The word 'regularly' suggests taking alternate letters from this phrase.
Answer: TIGERS | 'Regularly' indicates taking alternate letters from 'disTpatchIng zGbras' gives T-I-G-E-R-S, which are big cats.