Like one's regular paper round? (5)
I believe the answer is:
daily
This might be a double definition.
'like one's regular' is the first definition.
'daily' can be an answer for 'regular' (thesaurus). I am unsure of the 'like one's' bit.
'paper round?' is the second definition.
'daily' can be an answer for 'paper' (a daily is a kind of newspaper). I am not sure about the 'round?' bit.
Can you help me to learn more?
(Other definitions for daily that I've seen before include "regularly" , "Every twenty-four hours" , "Char" , "Cleaner; every 24 hours" , "Newspaper; cleaner" .)