Slightly tame show broadcast (8)
I believe the answer is:
somewhat
'slightly' is the definition.
(I know that slightly can be written as somewhat)
'tame show broadcast' is the wordplay.
'broadcast' indicates an anagram (letters scattered or cast around).
'tame'+'show'='tameshow'
'tameshow' is an anagram of 'SOMEWHAT'.
(Other definitions for somewhat that I've seen before include "Rather, a little" , "To some degree, sort of" , "To a small or moderate degree" , "To a certain extent" , "Moderately" .)