Display diplomacy, ousting Conservative as well (6)
I believe the answer is:
tattoo
'display' is the definition.
(I have seen 'Military display ' mean 'tattoo' so perhaps 'display' could also mean 'tattoo')
'diplomacy ousting conservative as well' is the wordplay.
'diplomacy' becomes 'tact' (tact can mean diplomacy or sensitivity).
'ousting' indicates named letters should be taken away.
'conservative' becomes 'C' (UK political abbreviation).
'as well' becomes 'too' (both can mean 'also').
'tact' with 'c' removed is 'tat'.
'tat'+'too'='TATTOO'
(Other definitions for tattoo that I've seen before include "piercing?" , "Military call and design on the skin" , "Indelible marks drawn on the skin" , "Drumbeat, or design on skin" , "Design worked on skin" .)