Letter delivered with sinking heart (5)
I believe the answer is:
delta
'letter' is the definition.
(Greek letter)
'delivered with sinking heart' is the wordplay.
'delivered' becomes 'dela' (I can't explain this - if you can you should give a lot more credence to this answer).
'with' indicates putting letters inside.
'sinking' becomes 'scuttling' (scuttle can mean to sink or scurry away).
'heart' indicates the central letters.
The middle of 'scuttling' is 't'.
'dela' going around 't' is 'DELTA'.
Can you help me to learn more?
(Other definitions for delta that I've seen before include "Comms code for 'd'" , "Greek letter in the shape of a triangle" , "Estuary area where river has split" , "Alluvial area - Greek letter" , "Multiple estuary" .)