Put simply, supremo will block harsh cuts (8)
I believe the answer is:
succinct
'put simply' is the definition.
'supremo will block harsh cuts' is the wordplay.
'supremo' becomes 'cinc' (Commander in Chief abbreviation).
'will block' is an insertion indicator.
'harsh' indicates an anagram.
'cuts' with letters rearranged gives 'suct'.
'cinc' put within 'suct' is 'SUCCINCT'.
(Other definitions for succinct that I've seen before include "Brief, precise" , "Briefly and clearly expressed" , "Concise, pithy" , "Brief, clear" , "Crisply brief" .)