Absorbed by Minister, Ministry ends (7)
I believe the answer is:
termini
'ends' is the definition.
(terminus is a kind of end)
'absorbed by minister ministry' is the wordplay.
'absorbed by' indicates a hidden word.
'TERMINI' is hidden in the letters of 'minister ministry'.
(Other definitions for termini that I've seen before include "End points of rail or bus routes" , "Starting points, limits" , "limits of service" , "Rail, bus stations" , "End stations" .)