Most likely, the easiest way to keep this card's effect in use as long as possible is to have both players have 0 cards in their hands, which is advantageous, since Fabled and The Fabled tend to have effects that discard from the hand or work better from a low hand (in terms of the number of cards in your hand).
After the effect of "Morphing Jar" (which would be beneficial to a Fabled Deck), There is a guarantee of an equal hand size.
Play spells and traps facedown if hand is larger than your opponent to use this effect to hinder your opponent.
If you can keep your hand size equal to your opponent by the end phase, you are likely to negate their first effect as they summon/activate their first card, more so towards late-game when they have few options.
Play cards that reduce your hand during your opponent's turn to keep up with changes in hand size, such as "Karma Cut", "Dust Tornado" or "Phoenix Wing Wind Blast". (But be very wary of your opponent using cards that can do the same.)
During your turn, you will want to keep your hand the same size as your opponent's so that you can negate any traps they might play. However, during your opponent's turn, they are likely to be playing cards from their hand so keep your hand 1 less then theirs when you end your turn and you will be able to negate the first card they play. If you can then play a few cards during your opponent's turn that drop your hand advantage, then you may be able to negate the first, second, and sometimes even third card your opponent plays.
Due to the wording on the card and the continous nature of this cards effect, this card will also negate and destroy counter traps as well, allowing you to activate effects as bait for their counter traps while still being able to use the effects. The usually unstoppable Super Polymerization can be stopped as well.
Example: Your opponent has "Solemn Judgment" set and "Ally of Justice Catastor" (being the main wall to deal with) on the field and a hand size of 3, while you have "The Fabled Unicore" and a set "Raigeki Break" (which you had set last turn) and a hand size of 4. You activate "Raigeki Break" and discard a card as a cost which gives you an equal hand to your opponent, targeting "Ally of Justice Catastor". In an attempt to save the main defense, the opponent plays "Solemn Judgment" and pays half his Life Points. During resolution "Solemn Judgment" is negated and destroyed by the effect of "The Fabled Unicore" and "Raigeki Break" destroys "Ally of Justice Catastor".
Use Trap cards that allow you to draw, such as "Jar of Greed", "Legacy of Yata-Garasu" or "Reckless Greed" to increase the number of cards in your hand to match that of your opponents. Chain these to Spell or Trap cards to force your opponent to waste them.
This card is deadly against Infernity decks: They always tries to keep their hand at 0, so you can also try to empty your hand. Since their hand is 0 and they are heavily dependent on their effects, your opponent's options are extremely limited.