No rest with guy's new child (9)
I believe the answer is:
youngster
'child' is the definition.
(synonyms)
'no rest with guy's new' is the wordplay.
'with' says to put letters next to each other.
'new' is an anagram indicator.
'no'+'rest'='norest'
'norest' put after 'guy' is 'guynorest'.
'guynorest' with letters rearranged gives 'YOUNGSTER'.
(Other definitions for youngster that I've seen before include "tyke" , "one of tender years" , "Adolescent" , "Child, minor" , "Kid" .)