German poet’s idyll finally digested by Republican president (5)
I believe the answer is:
rilke
'german poet's' is the definition.
(German-language poet Rainer Maria Rilke)
'idyll finally digested by republican president' is the wordplay.
'finally' says to take the final letters.
'digested' indicates putting letters inside.
'by' is a charade indicator (letters next to each other).
'republican' becomes 'r' (abbreviation).
'president' becomes 'ike' (I've seen this before**).
The last letter of 'idyll' is 'l'.
'r' next to 'ike' is 'rike'.
'l' inserted within 'rike' is 'RILKE'.
(Other definitions for rilke that I've seen before include "Bohemian poet?" , "Rainer Maria --, Austrian poet" , "he once wrote" , "Rainer Maria ---, German poet" .)