Sailor follows old prime minister's guiding light (5,4)
I believe the answer is:
north star
'guiding light' is the definition.
(I've seen this before)
'sailor follows old prime minister's' is the wordplay.
'sailor' becomes 'tar' (slang term for a sailor).
'follows' is a charade indicator (letters next to each other).
'old prime minister' becomes 'norths' (I can't justify this - if you can you should give a lot more credence to this answer).
'tar' put after 'norths' is 'NORTH STAR'.
Can you help me to learn more?
(Other definitions for north star that I've seen before include "nickname of US State" , "guiding light" , "Polaris" , "Navigational aid" , "feature of Ursa Minor" .)