Cherish silence preserved by inner circle's last broadcast (8)
I believe the answer is:
enshrine
'cherish' is the definition.
(I've seen this before)
'silence preserved by inner circle's last broadcast' is the wordplay.
'silence' becomes 'sh' ('sh' is said to tell someone to be silent).
'preserved by' indicates putting letters inside (I've seen this in other clues).
'last' indicates one should take the final letters.
'broadcast' is an anagram indicator (letters scattered or cast around).
The final letter of 'circle' is 'e'.
'inner'+'e'='innere'
'innere' anagrammed gives 'enrine'.
'sh' put within 'enrine' is 'ENSHRINE'.
(Other definitions for enshrine that I've seen before include "Hold sacred - protect" , "Consider sacred" , "Preserve (something) in a form ensuring respect" , "Preserve as worthy of reverence" , "Protect and preserve in law" .)