Isn't entirely suggesting one should give up, when it's enclosed in short letter (8)

'isn't entirely suggesting one should give up when' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.

'enclosed in short letter' is the wordplay.
'enclosed' becomes 'quit' (I can't explain this - if you can you should give a lot more credence to this answer).
'in' indicates putting letters inside.
'short letter' becomes 'note' (synonyms).
'quit' inserted into 'note' is 'NOTQUITE'.

'it's' acts as a link.

Can you help me to learn more?