someone who is skillfully handling people.... Not really sincere, just trying to keep a conversation...fake, etc
talking about politics with people....
any other meaning?
I agree with Humble that some context would be helpful, but I suspect that the meaning of "practising" is analogous with "practising medicine" ('being a doctor professionally'), so that a practising politician is someone who actually does politics for a living, rather than someone who goes to a parish council meeting every other Thursday evening!
If you're learning American English, don't worry about my spelling; but over here the verb is practise.