I'm currently in a homebrew campaign and the DM has stated he doesn't mind my character using a circlet (what would essentially be her crown since she's a royal type) but it has to have some sort of symbolism. I read that an arcane focus could be a crystal so could I just have her still have her crown but the crystal as the focus and be embedded?
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The character will need to hold the circlet in their hand when using it as a focus. From the section on Material Components in Chapter 10 of the PHB:
A spellcaster must have a hand free to access a spell's material components - or to hold a spellcasting focus - but it can be the same hand that he or she uses to perform somatic components.
The exception to this rule would be a holy symbol, which a cleric can have displayed on a shield, for example.