Princess entertaining country's prime minister (8)
I believe the answer is:
disraeli
'prime minister' is the definition.
(Benjamin Disraeli, Victorian prime minister)
'princess entertaining country's' is the wordplay.
'princess' becomes 'di' (Princess Diana).
'entertaining' means one lot of letters goes inside another (inviting in, as for dinner).
'country' becomes 'israel' (Israel is an example).
'di' placed around 'israel' is 'DISRAELI'.
(Other definitions for disraeli that I've seen before include "Benjamin -, nineteenth century prime minister" , "Victorian prime minster" , "Ali dries out the old British prime minister" , "Victorian prime minister" , "Queen Victoria's favourite prime minister, d. 1881" .)