Social climber Carrie's endless struggle to hide Boris's temperament, conclusively (9)
I believe the answer is:
arriviste
'social climber' is the definition.
(I've seen this before)
'carrie's endless struggle to hide boris's temperament conclusively' is the wordplay.
'endless' means to look at the middle letters.
'struggle' becomes 'vie' (I've seen this before).
'to hide' indicates putting letters inside.
'conclusively' indicates one should take the final letters (the letter which concludes the word).
The centre of 'carrie' is 'arri'.
The last letters of 'boris temperament' are 'st'.
'vie' placed around 'st' is 'viste'.
'arri'+'viste'='ARRIVISTE'
(Other definitions for arriviste that I've seen before include "Ambitious self-seeker" , "Rare visit (anag) - person on the make" , "nouveaux riches" , "Social climber" , "Upstart" .)