Request is extremely legitimate (7)
I believe the answer is:
solicit
'request' is the definition.
(solicit can can mean to request something)
'extremely legitimate' is the wordplay.
'extremely' becomes 'so' ('so' can mean 'extremely' or 'very').
'legitimate' becomes 'licit' (synonyms).
'so'+'licit'='SOLICIT'
'is' acts as a link.
(Other definitions for solicit that I've seen before include "Accost - request" , "Proposition" , "Beg - hustle" , "Ask (favour)" , "Request, canvas" .)