Plain type of hospital shoots up (8)
I believe the answer is:
sanserif
'plain type' is the definition.
(san serif is a type of typeface)
'hospital shoots up' is the wordplay.
'hospital' becomes 'san' (short for sanatorium).
'shoots' becomes 'fires' (firing is a kind of shooting).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'fires' backwards is 'serif'.
'san'+'serif'='SANSERIF'
'of' is the link.
(Other definitions for sanserif that I've seen before include "Fairness (anag) - printing type" , "font" , "Type without projection on letters" , "Style of typeface" , "Printing type style" .)