Jungle Book role’s cut line in private (6)
I believe the answer is:
mowgli
'jungle book role's' is the definition.
(Mowgli is a character in The Jungle Book)
'cut line in private' is the wordplay.
'cut' becomes 'mow' (as in mowing a lawn).
'line' becomes 'l' (used when specifying particular lines from a poem).
'in' is an insertion indicator.
'private' becomes 'GI' (GI can informally mean a US soldier).
'l' inserted within 'gi' is 'gli'.
'mow'+'gli'='MOWGLI'
(Other definitions for mowgli that I've seen before include "Kipling character" , "boy reared by wolves" , "The Jungle Book hero" , "Jungle Book 'man-cub'" , "Jungle Book boy (Kipling)" .)