Live it up out with noted parent (5,3,4,3)
I believe the answer is:
paint the town red
'live it up' is the definition.
(both can mean to celebrate or party)
'out with noted parent' is the wordplay.
'out' indicates an anagram.
'with'+'noted'+'parent'='withnotedparent'
'withnotedparent' with letters rearranged gives 'PAINT THE TOWN RED'.
(Other definitions for paint the town red that I've seen before include "Go on a pub crawl" , "get rid of the blues?" , "enjoy celebration" , "Celebrate" .)