Shalom dear Rabbi.
Question: Can a Beit Din that will make conversions (koshe recognized), charged to the guiur? in the case of the rabbi may provide a necessary price for the person becomes?
Technically a Beit Din should not charge for a din torah etc., the custom is that they do charge because the Beit Din has expenses, and because the dayanim are spending time, when they could have been earning money in order to rule on the din torah. A Beit Din for geirus although it is preferable that they don’t charge, however they are allowed to charge, and this is the common practice. It is better though when the dayanim are not being paid directly, and the person paying the fee, pays the office, and the dayan receives a set salary.
Regarding a private Rov he can also take a nominal amount called sechar tircha, or to pay expenses, however if it is a large amount it could be an issue, because the money might be a form of a bribe for him to do the geirus when otherwise it wouldn’t be accepted.
Teshuvos V’hanhagos 1-612, Mishnas Hager 3-28, Conversation with R’ M. Klein shlit”a, author of Mishnas Hager, and R Nachum Eisenstein shlit”a.