Does a spell that says target player draw a card give priority back before the draw resolves?

When a spell or ability resolves, it executes all of its instructions in order without any player receiving priority in between steps of that resolution. This is established by CR 608.2, which states that the spell or ability performs the actions described on the card as part of a single, uninterrupted resolution process.

Priority is only passed after a spell or ability has finished resolving (CR 116.3). So if a spell says 'Target player draws a card,' the draw happens as part of resolution, and only once the entire spell is done do players get the chance to respond again.

This means no player can cast an instant or activate an ability 'in between' the spell being cast and the draw actually happening — by the time anyone gets priority again, the card has already been drawn and the spell is in the graveyard.

Concrete example: Your opponent casts Divination (draw two cards). You cannot cast a spell like Thought Hemorrhage targeting them 'before they draw' once Divination has started resolving — both draws happen as part of Divination's resolution, and priority only returns to you after both cards are already in their hand.

If you want to prevent the draw, you must counter the spell or otherwise stop it before it begins to resolve, while it is still on the stack and players still have priority (CR 116.1, CR 601.2).