[RPG] Can Protection Fighting Style Be Used After The Roll

No.

Each of these abilities provide a separate reaction and neither provides a way to combine them.

Oath of the Crown provides a similar effect

If your player is interested in playing a style where they focus on defending others you may be interested in the Oath of the Crown Paladin from Sword Coast Adventure's Guide. At 7th level they gain Divine Allegiance which lets them use their reaction to take the damage for another creature giving a similar effect to this combination.

You don't have to use an action to ready either of those. Both of them use your reaction.

Protection Fighting Style:

When a creature you can see attacks a target other than you that is within 5 feet of you, you can use your reaction to impose disadvantage on the attack roll.

And Sentinel feat:

When a creature within 5 feet of you makes an attack against a target other than you (and that target doesn’t have this feat), you can use your reaction to make a melee weapon attack against the attacking creature.

In case you don't know what a reaction is, it's this:

Certain special abilities, spells, and situations allow you to take a special action called a reaction. A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else’s. The opportunity attack is the most common type of reaction.

When you take a reaction, you can’t take another one until the start of your next turn.

So, in summary, you don't have to use your action to ready either of these. However, since both of them require you to use your reaction, you can't use both of them together. When an enemy attacks one of your allies, you can choose to use either of them, but not both.