Section of roast rib alarmed family (6)
I believe the answer is:
tribal
'family' is the definition.
(both can mean relating to one's family)
'section of roast rib alarmed' is the wordplay.
'section of' says the answer is hidden in the clue.
'TRIBAL' is hidden in the letters of 'roast rib alarmed'.
(Other definitions for tribal that I've seen before include "Like certain social groups" , "belonging to close-knit group" , "Characteristic of social group" , "Of a traditional social group" , "Of a group of people related by blood" .)