It may enable people to make their mark in politics (6)
I believe the answer is:
ballot
This clue could be a double definition.
'it may enable people to make' is the first definition.
The definition suggests a singular noun which matches the answer.
'mark in politics' is the second definition.
The definition and answer can be both acts as well as being singular nouns.
Perhaps there's a link between them I don't understand?
'their' is the link.
Can you help me to learn more?
(Other definitions for ballot that I've seen before include "Poll" , "Referendum" , "Voting procedure" , "Document listing the alternatives to vote for" , "Election" .)