Yet, perhaps, deserve to be admitted, having boldness (8)
I believe the answer is:
temerity
'boldness' is the definition.
(I know that temerity is a type of boldness)
'yet perhaps deserve to be admitted' is the wordplay.
'perhaps' indicates an anagram.
'deserve' becomes 'merit' (synonyms).
'to be admitted' means one lot of letters goes inside another (inserted letters are admitted in).
'yet' with letters rearranged gives 'tey'.
'tey' going around 'merit' is 'TEMERITY'.
'having' acts as a link.
(Other definitions for temerity that I've seen before include "Front" , "Rashness, unreasonable contempt for danger" , "Cheek" , "Rashness, audacity" , "Overconfidence" .)