One might bite in indignation (4)
I believe the answer is:
gnat
'one might bite' is the definition.
'in indignation' is the wordplay.
'in' indicates the answer is hidden within the clue.
'GNAT' can be found hidden inside 'indignation'.
(Other definitions for gnat that I've seen before include "Small biting fly" , "Stinging insect" , "Insect often hovering over stagnant water" , "small irritant" , "Something that bites" .)