Hopeful mostly desire new President (7)
I believe the answer is:
wannabe
'hopeful' is the definition.
(synonyms)
'desire new president' is the wordplay.
'desire' becomes 'wan' (I can't explain this - if you can you should give a lot more credence to this answer).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'president' becomes 'Abe' (Abraham (Abe) Lincoln).
'wan'+'n'+'abe'='WANNABE'
'mostly' is the link.
This may not be correct. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for wannabe that I've seen before include "Ambitious person" , "Aspirant" , "hopeful" , "One ambitious to fit in, succeed" , "Aspiring film star possibly" .)