Live life outrageously — that shows confidence (6)
I believe the answer is:
belief
'confidence' is the definition.
(I've seen this before)
'live life outrageously' is the wordplay.
'live' becomes 'be' (synonyms).
'outrageously' indicates an anagram.
'life' with letters rearranged gives 'lief'.
'be'+'lief'='BELIEF'
'that shows' acts as a link.
(Other definitions for belief that I've seen before include "Tenet, creed" , "Religious conviction" , "Faith, credence" , "Faith, doctrine" , "Trust, faith (6)" .)