Arrogance of British leaving rubbish all over the place (6)
I believe the answer is:
hubris
'arrogance' is the definition.
(hubris is a kind of arrogance)
'british leaving rubbish all over the place' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'leaving' suggests deleting specific letters.
'all over the place' indicates an anagram.
'rubbish' with 'b' taken away is 'rubish'.
'rubish' with letters rearranged gives 'HUBRIS'.
'of' is the link.
(Other definitions for hubris that I've seen before include "Irrational" , "Arrogance or over-confidence" , "Overreaching pride" , "having an extremely big head?" , "Arogant pride and egotism" .)