Running races after rocket: that’s guts! (7)
I believe the answer is:
viscera
'guts' is the definition.
(I've seen this before)
'running races after rocket' is the wordplay.
'running' indicates an anagram.
'after' means one lot of letters go next to another.
'rocket' becomes 'vi' (the V-1 was a world war II flying bomb).
'races' with letters rearranged gives 'scera'.
'scera' after 'vi' is 'VISCERA'.
'that's' is the link.
(Other definitions for viscera that I've seen before include "organs inside" , "Abdominal organs -- cars vie (anag)" , "Entrails -- CIS rave (anag)" , "Internal organs, intestines" , "Guts" .)