Short letter sent out about end of prom sinking (10)
I believe the answer is:
settlement
'sinking' is the definition.
(sinking or settling down)
'short letter sent out about end of prom' is the wordplay.
'short' means to remove the last letter.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'about' indicates putting letters inside.
'end of' says to take the final letters.
The last letter of 'prom' is 'm'.
'letter' with its final letter removed is 'lette'.
'lette'+'sent'='lettesent'
'lettesent' with letters rearranged gives 'settleent'.
'settleent' placed around 'm' is 'SETTLEMENT'.
(Other definitions for settlement that I've seen before include "Hamlet - conclusion" , "Community - payment" , "local community" , "Working out" , "Outpost; agreement" .)