Hamper request to infiltrate live broadcast at the back (6)
I believe the answer is:
basket
'hamper' is the definition.
(I've seen this in another clue)
'request to infiltrate live broadcast at the back' is the wordplay.
'request' becomes 'ask' (to ask is to request something).
'to infiltrate' means one lot of letters goes inside another.
'live' becomes 'be' (synonyms).
'at the back' suggests the final letters (the letter at the back).
The final letter of 'broadcast' is 't'.
'ask' put within 'be' is 'baske'.
'baske'+'t'='BASKET'
(Other definitions for basket that I've seen before include "Shopper may have this" , "Woven container for carrying food etc" , "Woven receptacle" , "Container made of interwoven cane or wire" , "Container made of interwoven wire or canes" .)