I think these are correct but don't fully see the wordplay....
Relatively deprived? Finally speak out more - KINLESS as in 'Less Kin', but why 'Speak out More'?
Precisely surrounding vessel, caught deserter - TURNCOAT - If 'Vessel' = URN + C(aught) then that leaves 'TOAT for 'Precisely?
Contact a head supporting part of basic education - REACH (Contact) but I can't see any of the parsing.
Getting right article back ahead of time - RECEIPT - Again, I can't see any of it.
Clearly shows sex in Rome in drunken scene - EVINCES - It's an anagram of 'SCENE' + Vin but I've looked Vin up on Google Translator and nowhere does it say it = Sex in Latin or Italian.