The "do not replace" effect stacks with whatever "do not replace" clause the card itself has, so that the longest one wins out.
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Hagar Stone
G5Sabbat: While Hagar is ready, you get +1 hand size. While he is unlocked, you do not replace cards you play during your turn until he locks or your turn ends. Black Hand.
Rulings
The "do not replace" effect effectively reduces the hand size: additional draws (eg. Ashur Tablets) require a discard.
Black Hand is not a title, it is a trait unrelated to any sect. The trait is not lost if the vampire changes sect.