Edit: Revisions as spells are reexamined.
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A necromantic theme naturally features necromancers, which naturally features some necromancy spells. Here are the base list of necromancy spells designed for this theme, most often used by the magic items.
Spell List:
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DESIGN COMMENTARY
These spells are intended to cover a breadth of necromantic themes, such as blood (Cruor), Decomposition (Flash of Decay), Undeath (Flash of Decay), Undead creatures (Mummific Binds), Wizardry (Restless Necropolis).
Disembody Self is probably my favorite; dividing yourself into three smaller creatures for a brief time. Pretty good utility, kind of like a limited polymorph (three CR 1/4 unlike polymorphs's CR 9) for extra hit points plus a flock of familiars for scouting. See the fleshmire (upcoming) and skinmeld stat blocks.
Throat Rot and Cruor offer unique control options that encourage targets to either not cast spells or move, respectively. The operative word is "encourage," since they are unsaveble yet its low damage is wholly avoidable. It's kind of like heat metal. I've gone back and forth with Cruor because I feel unsaveable spells tend to start around 2nd-level to avoid introducing such swingy effects so early, but counter-examples like magic missile's auto-damage and entangle's difficult terrain is similar to what Cruor is doing. The damage swung between d4 and d8, and d6 probably won't break the game.
Restless Necropolis is a version of guards and wards and druid's grove but for necromancers. Mostly for flavor, but good for NPCs.
Withering Smite is the only option for Paladins and Rangers, to expand on the spell list availability. Otherwise pretty straightforward, like a more focused version of blinding smite or staggering smite (all converge on the main utility of imposing disadvantage on attack rolls).
Soul Swap is a total flavor spell, but has some combat use. At 7th level, it's kind of like a very short-duration dominate monster. Since dominate monster is a 1-hour 8th level spell, 7th level feels appropriate.
Ghostly Haunt and Mummific Binds are the extensions of Vampiric Touch. Ghostly Haunt is a very unique buff and/or debuff, using a mechanic not yet known before. Its utility allows casters to follow difficult targets, which is about as useful as (half of) dimension door, with the danger of being too close, so best used for gishes. Mummific Binds is a basic debuff option.