Exciting Rob, Eve's watch (7)
I believe the answer is:
observe
'watch' is the definition.
(observing is a kind of watching)
'exciting rob eve's' is the wordplay.
'exciting' indicates anagramming the letters.
'rob'+'eves'='robeves'
'robeves' with letters rearranged gives 'OBSERVE'.
(Other definitions for observe that I've seen before include "monitor" , "Notice or conform to, rules say" , "obey" , "Watch attentively" , "Notice, watch" .)