Easily persuaded president to drop subject (6)
I believe the answer is:
liable
'subject' is the definition.
(thesaurus)
'easily persuaded president to drop' is the wordplay.
'easily persuaded' becomes 'pliable'.
'president' becomes 'p' (common abbreviation eg in VP).
'to drop' indicates named letters should be taken away.
'pliable' with 'p' removed is 'LIABLE'.
(Other definitions for liable that I've seen before include "Legally answerable" , "Responsible at law" , "legally obliged, held responsible" , "Inclined" , "Likely" .)