By itself, dealing about 12 points of damage each round (assuming a hit) and healing only 5 or 6 points as a result is pretty weak though for a higher than 11 CR monster.  Making it as a Bonus action is better, IMO, b/c reactions are for opportunity attacks. Is vulnerability really that strong? So 22 or 24 damage average with 11 or 12 points of healing average.  If I restrict the Vampiric effect to once a round, not too strong. Esp if I tie necrotic vulnerability to a restricted healing on the same concentration spell, so that even though Vampiric is doing 6d6 damage a round, healing is only about 2d6 per round ( about 7 average ).

I think that creates a strong incentive to break the caster's concentration without being OP.

Or perhaps instead of Necro vulnerability on that concentration spel, make it a straight plus 3 necrotic damage, but stacking for each successful necrotic attack hit. So third successful necrotic hit by the same creature does plus 9.  

I wonder if you can use the Death Domain Divine Intervention with this. The spell does say "Make a melee spell attack against a creature within your reach. On a hit, the target takes 3d6 necrotic damage, and you regain hit points equal to half the amount of necrotic damage dealt." and Death Touch says "When the cleric hits a creature with a melee attack, the cleric can use Channel Divinity to deal extra necrotic damage to the target. The damage equals 5 + twice his or her cleric level". At level 5, which is when you can get Vampiric touch for the first time, that's at least 15 necrotic damage for a minimun of 18 to a max of 33.

You can make NPCs the same way you can make PCs. It says this in the DMG.

I'd just make a Life Cleric - Necromancer mix. Even without upcasting, the spell does 3d6, average 9 damage, and heal 4 (average) + 5 (disciple of life), plus additional 9 if you kill (Grim Harvest - have low HP minions it can use it on if needed). All while rocking 20 AC (full plate + shield). You could also make them an undead (undying fortitude). You now have a very hard to kill undead enemy that's siphoning life from the party members that can also have its own living (for grim harvest) and undead (animate dead) minions. 

Being a cleric, it can also cast Sanctuary on itself as a bonus action if it starts to lose. 

You can set the stats to whatever you need and provide it with decent non-concentration spells to support it, from both Wizard and Cleric spell lists to make some great combinations (like Misty Step so it can easily get into range). If this is a BBEG you can try lair actions which fit the mix, like one heals them and their minions and another necro-damages the party - further delving into the mix of Life and Death.

Just saying there's ways to build around and improve the spell's efficacy without even needing to tweak the spell. Just an option. ¯\_(ツ)_/¯