Why didn't the First Order jump ahead of the Resistance?

Why didn't the First Order jump ahead of the Resistance?

If you get the chance to watch the film again, you'll see that the First Order does in fact jump in front of the Resistance fleet, though, only for the first jump.

After this happens, Poe asks Leia if he can jump into a cockpit and blow stuff up (a joke to a previous comment of Leia's), she says yes, and then she yells a command to turn the ship around and to focus all shields on the ship's rear.

For all future jumps though, the First Order does show up just behind the Resistance.

It could be argued that, since the Resistance's ship has the ability to focus their shields at various sections of the ship, it doesn't really matter where the First Order first appears after exiting hyperspace since the Resistance can just turn around and refocus their shields accordingly, like they did the first time.

Why didn't the First Order jump ahead of the Resistance?

Main reason

When jumping to light speed, just before doing so, a series of calculations need to be made and a predetermined path is established. Within the context of the OP, it was mentioned that roughly a 30 second time difference existed between the Rebel fleet exiting hyperspace, and the First Order showing up just behind them. That being said, before jumping to light speed, the First Order had no way of knowing exactly where the Rebel fleet would be 30ish seconds in the future.

It's easily possible that, while the First Order was in hyperspace, the Rebel fleet could have significantly changed direction and/or their velocity, thus making it nearly impossible for the First Order to predict where they'd be, to then get in front of them. Being in space, the Rebel fleet could have literally moved in any direction.

Other reasons

1. To avoid the potentiality of a head-on collision between the two fleets, should the hyperspace exit point be overshot. It was shown quite clearly what happens when two ships collide while one of them is traveling at light speed.

2. Nothing major would be gained, other than maybe saving a few hours. The fuel supply of the Rebel fleet was already low, and with each jump to light speed it was depleting just that much more. At one point it was mentioned that they'll be out of fuel in 18 hours, of which General Hux commented that it's now just a waiting game.

From the script:

HUX: Ren, the Resistance have pulled out of reach. We can't cover you at this distance. Return to the fleet. What is the point of all this if we can't blow up three tiny cruisers?

PEAVEY: They are faster and lighter, sir. They can't lose us but they can keep at a range where our cannons are not effective against their shields.

HUX: Well, keep up the barrage. Let's at least remind them that we're still here.

PEAVEY: Very good sir.

HUX: They won't last long burning fuel like this. It's just a matter of time.

So the reason is that the resistance ships were able to out-manoeuvre the First Order's much larger vessels, but not ultimately escape from them due to lack of fuel and the ability to be tracked through hyperspace.

Jumping in front of the resistance wouldn't have helped much, they would just have moved away again. The First Order ships couldn't jump in too close for fear of what ultimately did happen - a collision at hyperspace speed.