Military supremo holds nothing up to get medical facility (6)
I believe the answer is:
clinic
'medical facility' is the definition.
(I've seen this in another clue)
'military supremo holds nothing up' is the wordplay.
'military supremo' becomes 'cic' (I can't justify this - if you can you should give a lot more credence to this answer).
'holds' is an insertion indicator.
'nothing' becomes 'nil' (eg nil is zero in football).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'cic' enclosing 'nil' is 'cinilc'.
'cinilc' backwards is 'CLINIC'.
'to get' is the link.
Can you help me to learn more?
(Other definitions for clinic that I've seen before include "Hospital department" , "Medical or political facility" , "Medical treatment centre" , "Place for medical treatment or political advice" , "Private hospital" .)