Bird starts to rummage on waste container (5)
I believe the answer is:
robin
'bird' is the definition.
(robin is a kind of bird)
'starts to rummage on waste container' is the wordplay.
'starts to' indicates taking the first letters.
'waste container' becomes 'bin' (I've seen this before).
The first letters of 'rummage on' is 'ro'.
'ro'+'bin'='ROBIN'
(Other definitions for robin that I've seen before include "Red-breasted songbird" , "Batman's assistant" , "Christmas-card bird" , "Batman's companion" , "Bird; man's name" .)