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 in another clue)
'sailor follows old prime minister's' is the wordplay.
'sailor' becomes 'tar' (term for a sailor).
'follows' means one lot of letters go next to another.
'old prime minister' becomes 'norths' (I am not sure about this - if you are sure you should believe this answer much more).
'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" .)