Tailor having a bit of modesty left (5)
I believe the answer is:
style
'tailor' is the definition.
('style' can be a synonym of 'tailor')
'a bit of modesty left' is the wordplay.
'a bit of' says the answer is hidden in the clue (I've seen 'a bit' mean this (the answer is formed by a bit of the clue)).
'STYLE' is hidden within 'modesty left'.
'having' acts as a link.
(Other definitions for style that I've seen before include "Superior quality" , "Technique" , "Official title; manner" , "Manner; elegance" , "Chic" .)