Royal papers about popular Conservative leader (8)
I believe the answer is:
princess
'royal' is the definition.
(princess royal is a kind of royal)
'papers about popular conservative leader' is the wordplay.
'papers' becomes 'press' (I've seen this before).
'about' indicates putting letters inside.
'popular' becomes 'in'.
'conservative leader' becomes 'c' (I've seen this in other clues).
'in'+'c'='inc'
'press' going around 'inc' is 'PRINCESS'.
(Other definitions for princess that I've seen before include "Attractive woman" , "Royal girl" , "Female aristocrat" , "She's royal" , "Royal personage" .)