For young lady, I have shortened a letter (7)
I believe the answer is:
missive
'a letter' is the definition.
(I know that letter can be written as missive)
'for young lady i have shortened' is the wordplay.
'for young' becomes 'mis' (I can't justify this - if you can you should give a lot more credence to this answer).
'lady' becomes 'Ms' (alternative to Miss or Mrs).
'i have' becomes 'I've' (contraction of 'I have').
'shortened' means to remove the first letter.
'ms'+'ive'='msive'
'msive' with its first letter taken off is 'sive'.
'mis'+'sive'='MISSIVE'
Can you help me to learn more?
(Other definitions for missive that I've seen before include "message" , "Letter" , "intelligence in this?" .)