Band ultimately ignores a request for silence (4)
I believe the answer is:
sash
'band' is the definition.
(I know that sash is a type of band)
'ultimately ignores a request for silence' is the wordplay.
'ultimately' indicates one should take the final letters.
'request for silence' becomes 'sh' ('sh' is used to tell someone to be quiet).
The last letter of 'ignores' is 's'.
's'+'a'+'sh'='SASH'
(Other definitions for sash that I've seen before include "Baldrick" , "Strip of cloth worn round the waist" , "(Uniform) strip; window-frame" , "Type of sliding window" , "Ribbon worn over the shoulder" .)