Yet perhaps deserve to be admitted, showing boldness (8)
I believe the answer is:
temerity
'boldness' is the definition.
(temerity is a kind of boldness)
'yet perhaps deserve to be admitted' is the wordplay.
'perhaps' is an anagram indicator.
'deserve' becomes 'merit' ('merit' can be a synonym of 'deserve').
'to be admitted' indicates putting letters inside.
'yet' with letters rearranged gives 'tey'.
'tey' placed around 'merit' is 'TEMERITY'.
'showing' acts as a link.
(Other definitions for temerity that I've seen before include "Boldness, audacity" , "Presumption" , "Rash boldness" , "Yet merit may lead to rashness" , "Audacity or nerve" .)