Diverts a minister’s premier applications (6)
I believe the answer is:
amuses
'diverts' is the definition.
('amuse' can be a synonym of 'divert')
'a minister's premier applications' is the wordplay.
'premier' suggests taking the first letters.
'applications' becomes 'uses' (I've seen this before).
The first letter of 'ministers' is 'm'.
'a'+'m'+'uses'='AMUSES'
(Other definitions for amuses that I've seen before include "Diverts" , "Makes (someone) laugh" , "provides entertainment" , "Entertains" .)