Person in the job is popular, with Latin flair (9)
I believe the answer is:
incumbent
'person in the job' is the definition.
(person currently in a job)
'popular with latin flair' is the wordplay.
'popular' becomes 'in' (something that's 'in' is fashionable).
'with' becomes 'cum' ('with' in Latin).
'latin flair' becomes 'bent' (bent can mean a talent or flair for something. I am not sure about the 'latin' bit.).
'in'+'cum'+'bent'='INCUMBENT'
'is' is the link.
Can you help me to learn more?
(Other definitions for incumbent that I've seen before include "Functionary" , "Current holder of post" , "What's obligatory" , "Mandatory" , "Necessary - office-holder" .)