Caught right in the trap, don’t look at all despondent (4)
I believe the answer is:
grin
'don't look at all despondent' is the definition.
I can't judge whether this definition defines the answer.
'caught right in the trap' is the wordplay.
'caught right' becomes 'r' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'in the' indicates putting letters inside.
'trap' becomes 'gin' (gin trap is a kind of animal trap).
'r' going within 'gin' is 'GRIN'.
Can you help me to learn more?
(Other definitions for grin that I've seen before include "Cheesy smile?" , "Look pleased" , "Toothy smile" , "Smile - all that could be seen of the vanishing Cheshire Cat" , "Smile while pulling back the lips" .)