R 24:

Further, you can't share spells with a familiar any more. You can cast a touch spell through your familiar, such that only the familiar needs to touch the target, not you. You can also share spells with a creature you summon via the paladin spell Find Steed, if you are mounted on the steed.

A paladin with access to the Shield spell somehow (such as via the Magic Initiate feat or multiclassing) who is hit by an attack could cast Shield and share it with her mount, and both would then benefit from the +4 to AC for the spell's duration, but said paladin could still not cast Shield in reaction to the mount being hit.