Informer keeps president absorbed (4)
I believe the answer is:
rapt
'absorbed' is the definition.
('rapt' can be a synonym of 'absorbed')
'informer keeps president' is the wordplay.
'informer' becomes 'rat' ('rat' can be a synonym of 'informer').
'keeps' is an insertion indicator.
'president' becomes 'p' (common abbreviation eg in VP).
'rat' going around 'p' is 'RAPT'.
(Other definitions for rapt that I've seen before include "Delighted" , "Absorbed, fascinated" , "Ecstatic in part" , "Spellbound in part" , "'Transported, entranced (4)'" .)