Many rabbis are Kohaniim and have no problems or restrictions because of it. However, there are restrictions for a Kohain when it comes to officiating at funerals.

Some rabbis who are Kohains will not enter any structure or room in which there is a deceased person's body...However, they can conduct the funeral service from outside the room. At the cemetery, most rabbis who are Kohains will not walk on the grounds and, often officiate from outside the gates. Others, however, will walk on the pavement, which is not holy ground per se, and officiate from there.