Engineers broadcast dislike (6)
I believe the answer is:
resent
'dislike' is the definition.
(to resent is to dislike or begrudge)
'engineers broadcast' is the wordplay.
'engineers' becomes 're' (abbreviation for Royal Engineers).
'broadcast' becomes 'sent' (sent or transmitted as a broadcast).
're'+'sent'='RESENT'
(Other definitions for resent that I've seen before include "Feel bitter or indignant about" , "Dispatched again; feel bitterness at" , "Feel indignation at" , "grudge" , "given another posting?" .)