Undead Fortitude. If damage reduces the zombie to 0 hit points, it must make a Constitution saving throw with a DC of 5 + the damage taken, unless the damage is radiant or from a critical hit. On a success, the zombie drops to 1 hit point instead.

Infection.  A humanoid bitten by an Infectious Zombie makes a DC 13 Con save.  On fail they lose 1d6 max hit points and lose 1d6 to their HP max per day.  A bitten humanoid who dies rises 1d4 hours later as a zombie, unless the humanoid is restored to life or its body destroyed.  A spell like Greater Restoration, Remove Disease or Wish can remove the infection.  

Slam. Melee Weapon Attack: +3 to hit, reach 5 ft., one target. Hit: 4 (1d6 + 1) bludgeoning damage.

Bite. Melee Weapon Attack: +3 to hit, reach 5 ft., one target. Hit: 4 (1d6 + 1) piercing damage.  *See Special Trait: Infection*