Trump on island excited English press (9)
I believe the answer is:
importune
'press' is the definition.
(thesaurus)
'trump on island excited english' is the wordplay.
'island' becomes 'i' (geographical abbreviation).
'excited' is an anagram indicator.
'english' becomes 'E' (abbreviation as in OED).
'trump'+'on'+'i'='trumponi'
'trumponi' anagrammed gives 'importun'.
'importun'+'e'='IMPORTUNE'
(Other definitions for importune that I've seen before include "Make insistent requests for entropium" , "Persistently request" , "Solicit" , "Hound" , "Harry" .)