Good and bad rounds start off Robinson's quiz (5)
I believe the answer is:
grill
'quiz' is the definition.
(subject to questioning)
'good and bad rounds start off robinson's' is the wordplay.
'good' becomes 'g' (abbreviation).
'and' says to put letters next to each other.
'bad' becomes 'ill' (similar in meaning).
'rounds' indicates putting letters inside.
'start off' indicates taking the first letters.
The first letter of 'robinsons' is 'r'.
'g'+'ill'='gill'
'gill' enclosing 'r' is 'GRILL'.
(Other definitions for grill that I've seen before include "Interrogate - cook" , "Seriously question" , "Question aggressively" , "Framework of metal bars" , "Grating" .)