One piece of writing in career is unconvincing (6)
I believe the answer is:
flimsy
'unconvincing' is the definition.
(I know that unconvincing can be written as flimsy)
'one piece of writing in career' is the wordplay.
'one' becomes 'i' (Roman numeral).
'piece of writing' becomes 'ms' (abbreviation for manuscript).
'in' is an insertion indicator.
'career' becomes 'fly' (both can mean to veer uncontrollably).
'i'+'ms'='ims'
'ims' placed into 'fly' is 'FLIMSY'.
'is' acts as a link.
(Other definitions for flimsy that I've seen before include "Fragile; weak" , "Light and thin, material or argument, perhaps" , "Not strong" , "Insubstantial, light and thin" , "Light and thin, fragile" .)