Letters beginning each numbered clue offer Des’s excuse, duly disguised (7)
I believe the answer is:
encoded
'disguised' is the definition.
(disguised in code)
'letters beginning each numbered clue offer des's excuse duly' is the wordplay.
'letters beginning' indicates taking the first letters.
The first letters of 'each numbered clue offer dess excuse duly' is 'ENCODED'.
(Other definitions for encoded that I've seen before include "Deed con (anag.)" , "formed in a difficult-to-understand way" , "In cryptic version" , "as secrets are dispatched?" .)