“Dragunity” is an archetype of Dragon and Winged Beast monsters whose effects mainly revolve around equipping the Level 3 or lower Tuner monsters to the higher Level non-Tuner ones. Once the Level 3 or lower monsters are equipped, there are multiple ways to Special Summon them from the Spell & Trap Zone, giving you access to various Synchros.
It has definitely been a while since the last time Dragunity Synchro has seen competitive play in Duel Links, but the new Structure Deck EX Dragunity Overdrive might be what the archetype needs to be relevant again.
By discarding 1 “Dragunity” card, Dragunity Senatus allows you to equip to it 1 “Dragunity” Tuner directly from your Deck.
If you activate Dragunity Senatus’s effect, you cannot Special Summon any non-Dragon monsters from the Extra Deck for the rest of the turn, so, despite its name, you will not be able to Synchro Summon Brionac, Dragon of the Ice Barrier.
Upon being Synchro Summoned, Vajrayana will allow you to equip Phalanx (or any other Level 3 or lower “Dragunity” Dragon monster in your Graveyard) to it.
Now, if it’s the 1st Turn, you might want to Synchro Summon Stardust Spark Dragon.
When Dragunity Aklys is Normal Summoned, you can Special Summon 1 “Dragunity” monster from your hand, and then equip it with Aklys.
Once per turn, Dragunity Militum allows you to Special Summon 1 “Dragunity” card from your Spell & Trap Zone.
If you Summon Vajrayana, you can equip to it Aklys from the Graveyard, and then send it back to the Graveyard to double its ATK until the end of the turn. When Aklys is sent to the Graveyard, it allows you to target 1 card on the field and destroy it. Get rid of your opponent’s monsters and attack directly for massive damage.
I’ve already mentioned this card a couple times, but I need to emphasize just how good it is: if you equip Dragunity Knight - Vajrayana with this card, you will be able to equip it with Dragunity Aklys from the deck, increase its ATK by its Level x100 (600) and make it immune to Trap Cards.
If you are not convinced yet, let me add one more thing: if you then send Dragunity Aklys to the Graveyard with Dragunity Knight - Vajrayana’s effect, you will be able to destroy a card on the field and double Vajrayana’s current ATK, making a 5000 ATK monster immune to Trap Cards. Honestly the opponent has to stop you before you get to this point, unless you are playing against a Spellbook player.
By banishing 1 “Dragunity” monster from your Graveyard, Dragunity Knight - Ascalon allows you to target 1 monster your opponent controls and banish it. This would be a pretty underwhelming effect for a Level 10 Synchro that even requires a specific Tuner if it wasn’t for the fact that it’s not limited to a “once per turn” use.
As long as you have “Dragunity” monsters in your Graveyard to banish, you can keep on activating this effect.
If this Synchro Summoned card in its owner's control is destroyed by an opponent's card, you can Special Summon 1 "Dragunity" Synchro Monster with 3000 or less ATK from your Extra Deck.
Since this is treated as a Synchro Summon, if you use Ascalon’s effect to Summon Dragunity Knight - Barcha or Dragunity Knight - Vajrayana, you will be able to activate their effects.
I’ve already explained what you can do with this card, so I’m not going to repeat myself, the only thing that should be noted is that its effect doubles its “current” ATK and not its original ATK.
Once per turn, during either player’s turn, Stardust Spark Dragon allows you to target 1 face-up card you control; once during that turn, that card cannot be destroyed by battle or card effect. You can respond to Treacherous Trap Hole by activating this effect, targeting even Stardust Spark Dragon itself, a prevent it from being destroyed. Stardust Spark Dragon is essentially a fairly safe Turn 1 play.