Sure of oneself, not half jovial in private (12)
I believe the answer is:
confidential
'private' is the definition.
(similar in meaning)
'sure of oneself not half jovial' is the wordplay.
'sure of oneself' becomes 'confident' (being confident is being sure of yourself).
'not half' indicates taking half.
'jovial' with half the letters taken is 'ial'.
'confident'+'ial'='CONFIDENTIAL'
'in' acts as a link.
(Other definitions for confidential that I've seen before include "Intended to be kept secret" , "not expecting publication" , "Classified" , "Like T.S. Eliot's clerk" , "Graham Greene's agent" .)