Annoying person; destructive insect (4)
I believe the answer is:
pest
<span class="explanation-format__ClueExplanation">This clue is a double definition.<br/ ><br/ >'<span class="explanation-format__original">annoying person</span>' is the first definition.<br/ ><span class="explanation-format__explanation">(pest can mean an annoying person)</span><br/ ><br/ >'<span class="explanation-format__original">destructive insect</span>' is the second definition.<br/ ><span class="explanation-format__explanation">(pest can mean insect that damages crops)</span><br/ ><br/ ></span>
(Other definitions for pest that I've seen before include "Annoying creature" , "A nuisance - step on it" , "Destructive insect or nuisance" , "Destructive creature" , "Annoying person" .)