Monkey rushes all over the place (6)
I believe the answer is:
rhesus
'monkey' is the definition.
(rhesus monkey is a kind of monkey)
'rushes all over the place' is the wordplay.
'all over the place' indicates anagramming the letters.
'rushes' anagrammed gives 'RHESUS'.
(Other definitions for rhesus that I've seen before include "Kind of monkey (or factor)" , "Type of macaque" , "Blood type or sort of monkey" , "Small Asian macaque" , "King, in Greek mythology" .)