Lurk shiftily in the Ministry, making routine progress (4,3)
I believe the answer is:
milk run
'routine progress' is the definition.
The definition suggests a singular noun which matches the answer.
'lurk shiftily in the ministry' is the wordplay.
'shiftily' indicates an anagram (I've seen this in other clues).
'in the' means one lot of letters goes inside another.
'ministry' becomes 'min' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'lurk' with letters rearranged gives 'lkru'.
'lkru' going inside 'min' is 'MILK RUN'.
'making' acts as a link.
Can you help me to learn more?
(Other definitions for milk run that I've seen before include "routine trip" , "Routine journey" , "Routine flight" .)