Piece of equipment that could make mum more embarrassed (8)
I believe the answer is:
shredder
'piece of equipment' is the definition.
'mum more embarrassed' is the wordplay.
'mum' becomes 'sh' (I've seen this in other clues).
'more embarrassed' becomes 'redder'.
'sh'+'redder'='SHREDDER'
'that could make' acts as a link.
(Other definitions for shredder that I've seen before include "Document destroyer" , "Device for destroying documents" , "destroyer of sensitive material" , "Paper-cutter" , "one destroys paper" .)