There are is not a special priesthood that is closer to God then the individual Christian, there are only individual spiritual gifts.
5Ye also, as lively stones, are built up a spiritual house, an holy priesthood, to offer up spiritual sacrifices, acceptable to God by Jesus Christ.and see Jn 20:21-23
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9But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light;
21Then said Jesus to them again, Peace be unto you: as my Father hath sent me, even so send I you.Jesus communicated this ability to the Apostles, as mediators
22And when he had said this, he breathed on them, and saith unto them, Receive ye the Holy Ghost:
23Whose soever sins ye remit, they are remitted unto them; and whose soever sins ye retain, they are retained.
In fact, if you may pray on behalf of a fellow Christian, why can't priests do that?