Cook right inside grill (5)
I believe the answer is:
broil
'grill' is the definition.
(I've seen this before)
'cook right inside' is the wordplay.
'cook' becomes 'boil' (boiling is a kind of cooking**).
'right' becomes 'r' (common abbreviation).
'inside' indicates putting letters inside.
'boil' going around 'r' is 'BROIL'.
(Other definitions for broil that I've seen before include "Maybe grill" , "Be extremely hot" , "overheat?" , "stew" , "American heat" .)