Insect let out to chase another (6)
I believe the answer is:
beetle
'insect' is the definition.
(beetle is a kind of insect)
'let out to chase another' is the wordplay.
'out' means to remove the last letter.
'to chase' says to put letters next to each other.
'another' becomes 'beet' (I can't explain this - if you can you should believe this answer much more).
'let' with its final letter removed is 'le'.
'le' put after 'beet' is 'BEETLE'.
(Other definitions for beetle that I've seen before include "Lee bet he could be an insect" , "Insect (from Colorado?)" , "Heavy wooden mallet for an insect" , "Let bee buzz around this insect" , "Insect; dice game" .)