Reactionary Portuguese master turning in back gate in a certain style (10)
I believe the answer is:
postmodern
'in a certain style' is the definition.
(postmodernism is an artistic style)
'reactionary portuguese master turning in back gate' is the wordplay.
'reactionary portuguese master turning' becomes 'mod' (I can't justify this - if you can you should give a lot more credence to this answer).
'in' indicates putting letters inside.
'back gate' becomes 'postern' (I've seen this in another clue).
'mod' going inside 'postern' is 'POSTMODERN'.
(Other definitions for postmodern that I've seen before include "Of late twentieth century arts style" , "style incorporating classical features" , "In a late 20th-century style" , "artistic style" , "Late twentieth century style of art/architecture" .)