Don't notice that I have added to the letter (7)
I believe the answer is:
missive
'the letter' is the definition.
(synonyms)
'don't notice that i have added' is the wordplay.
'don't notice' becomes 'miss' (I can't explain this - if you can you should give a lot more credence to this answer).
'that i have' becomes 'ive'.
'added' means one lot of letters go next to another.
'miss'+'ive'='MISSIVE'
'to' acts as a link.
Can you help me to learn more?
(Other definitions for missive that I've seen before include "message" , "Letter" , "intelligence in this?" .)