Handle fellows with primarily tactful management (9)
I believe the answer is:
treatment
'management' is the definition.
(treatment is a kind of management)
'handle fellows with primarily tactful' is the wordplay.
'handle' becomes 'treat' (synonyms).
'fellows' becomes 'men' (fellow can mean a man).
'with' says to put letters next to each other.
'primarily' says to take the initial letters.
The first letter of 'tactful' is 't'.
'treat'+'men'+'t'='TREATMENT'
(Other definitions for treatment that I've seen before include "Management of something, illness say" , "The handling or management of something" , "NHS care?" , "Maintenance work" , "Handling - therapy" .)