Restrictive strap that keeps suit up (8)
I believe the answer is:
stifling
'restrictive' is the definition.
(thesaurus)
'strap that keeps suit up' is the wordplay.
'strap' becomes 'sling'.
'that keeps' indicates putting letters inside.
'suit' becomes 'fit' (synonyms).
'up' says the letters should be written backwards (in down clue: letters go upwards).
'fit' reversed gives 'tif'.
'sling' placed around 'tif' is 'STIFLING'.
(Other definitions for stifling that I've seen before include "Flings it in suffocating manner" , "close?" , "Unpleasantly hot or airless" , "Oppressively hot and airless" , "Oppressively hot and humid" .)