Detective's engagement must be a let-down (14)
I believe the answer is:
disappointment
'a let-down' is the definition.
(I've seen this before)
'detective's engagement' is the wordplay.
I cannot really see how this works, but
'detective's' could be 'dis' (Detective Inspector) and 'dis' is present in the answer.
'engagement' could be 'appointment' ('appointment' can be a synonym of 'engagement') and 'appointment' is located in the answer.
No letters remain.
This explanation may well be incorrect...
'must be' is the link.
Can you help me to learn more?
(Other definitions for disappointment that I've seen before include "Frustrating thing" , "Let-down" , "Setback" , "Frustration" , "unhappiness" .)