In a Cult game, there’s no way for evils to fake Telepathy (whereas in an Unseen game, The Illusionist has it, so at least there’s a chance the Psychic could be converted.)
I suggest giving Telepathy to the Cult to make it a bit harder for Psychics to claim and to generally let them play tricks. Yes, a Psychic doesn’t have a hard time proving, but it’d still be nice if a Psychic in a Cult game couldn’t instantly, 100% prove they weren’t converted at the push of a button.
Of course, the obvious first choice would be to give it to The Apostle, which the Psychic converts into. The problem is that the Apostle lacks a free day ability slot - however, one option might be to combine Cult Pressure and Cult Numbers into one ability; which one occurs would depend on when you push its button (push it before a trial, it has the Cult Pressure effect; push it during a trial, it has the Cult Numbers effect.)
Another option would be to wedge it into another Cult member - not as ideal, but it would at least keep the Psychic from 100% confirming that they’re not converted. There’s free Day ability slots on almost every other Cult role, so any of them could work.