Centre right is showing overconfidence (6)
I believe the answer is:
hubris
'overconfidence' is the definition.
(thesaurus)
'centre right is' is the wordplay.
'centre' becomes 'hub' (hub is a kind of centre).
'right' becomes 'r' (common abbreviation).
'hub'+'r'+'is'='HUBRIS'
'showing' acts as a link.
(Other definitions for hubris that I've seen before include "Arrogant pride, from the Greek" , "Overbearing pride or presumption" , "Arogant pride and egotism" , "The pride that goes before a fall" , "show of arrogance" .)