Here's an attempt to get Quest Paladin off the ground by using the new tools available to us that might help the archetype. 

Where's the new cards?

and technically . 

The only anti-synergy being Drek'Thar summoning Ivus, the Forest Lord so Ivus might be removed if he's not performing. Bare in mind Murgurgle Prime can deactivate Drek'Thar if he's in your deck. Best play Drek'Thar beforehand.

Mulligan

First Day of School, Sword of the Fallen, Alliance Bannerman. We can also keep Dun Baldar Bridge if we have some other 1 drops to play. Ivus, the Forest Lord is good to keep to avoid the anti-synergy as mentioned above.

The ideal first turns are playing the Quest first ofc, followed by First Day of School. If you want to be greedy, best hold as many minions in hand to get buffs from Alliance Bannerman. 

If you started second with the coin, try play Dun Baldar Bridge on 3 for a devastating turn 4 Drek'Thar. 

Reasons for secrets: We want decent value from Drek'Thar with our only bad summon being Ivus. This makes secrets more valuable to progress the quest and don't be afraid to use Sword of the Fallen to pull secrets from the deck. It can only pull 4 secrets total, while we have a total of 16 1-drops (if you include the minions generated from First Day of School). 

Gameplay

The best time to throw as many minions on the field will be during the Dun Baldar Bridge turns to get as many buffs as possible and overwhelm the opponent. Saidan the Scarlet gets +4/+4 and turns into a 3 mana 6/6 with rush, who can get bigger if you hand buff him with Alliance Bannerman. 

Rally! is also great but only use it after a good few 3 drops have died and Murgur Murgurgle as he's our only 2-drop. 

The Quest can help close out games and summoning 2 silver hands after Lightborn Cariel is played while Dun Baldar Bridge is active leads to some juicy 5/5 boys. 

The main game plan is aggro, but we can still be greedy to get more hand buffs, or wait for those Dun Baldar Bridge turns. The secrets help in this regard for a bit of stall. 

Closing Thoughts

This deck probably won't be great but I've always wanted Rise to the Occasion to be good and see some play. Lets hope with the new Fractured in Alterac Valley cards, it might be a force to be reckoned with.... minus the Reckoning.