Hollow Conservative greeting (4)
I believe the answer is:
cave
'hollow' is the definition.
(caving is a kind of hollowing)
'conservative greeting' is the wordplay.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'greeting' becomes 'ave' (I've seen this before).
'c'+'ave'='CAVE'
(Other definitions for cave that I've seen before include "Aladdin, Fingal, had one" , "Primitive dwelling" , "Troglodyte's home" , "Hollow - warning" , "Watch out" .)