Short passage not including covering letter, ultimately (7)
I believe the answer is:
excerpt
'short passage' is the definition.
(I've seen this before)
'not including covering letter ultimately' is the wordplay.
'not including' becomes 'except' (I've seen this before).
'covering' indicates putting letters inside.
'ultimately' indicates one should take the final letters.
The last letter of 'letter' is 'r'.
'except' going around 'r' is 'EXCERPT'.
(Other definitions for excerpt that I've seen before include "A passage from, music or book" , "Piece of work" , "Just a few words" , "1D [CLIP]" , "Piece selected from a film" .)