What’s outrageous in second phrase on family arms (5)
I believe the answer is:
motto
'phrase on family arms' is the definition.
(I've seen this before)
'what's outrageous in second' is the wordplay.
'what's outrageous' becomes 'OTT' (short for over the top).
'in' indicates putting letters inside.
'second' becomes 'mo' (both are short periods of time).
'ott' inserted within 'mo' is 'MOTTO'.
(Other definitions for motto that I've seen before include "Watchword" , "Shibboleth" , "Slogan encapsulating self-image" , "Cracker slip" , "Brief guiding rule" .)