Detective came up after medic got apparatus to supply nutrients (4)
I believe the answer is:
drip
'apparatus to supply nutrients' is the definition.
I can't tell whether this definition defines the answer.
'detective came up after medic' is the wordplay.
'detective' becomes 'PI' (private investigator).
'came up' says the letters should be written in reverse (I've seen 'coming up' mean this (in a down clue, letters go up)).
'after' means one lot of letters go next to another.
'medic' becomes 'dr' (doctor).
'pi' back-to-front is 'ip'.
'ip' put after 'dr' is 'DRIP'.
'got' acts as a link.
Can you help me to learn more?
(Other definitions for drip that I've seen before include "Leak from tap" , "Fall in small blobs" , "Fall in droplets -- weedy person" , "Wimp" , "Slow leak" .)