Base Class: Wizard
The wizards of the School of Chronomancy use the raw arcane power they possess to affect the flow of time around them, ripping portals into the flow of time so that they might briefly glimpse the future, the past, or even alternate realities from their own.
Foresight
Beginning when you choose this school at level 2, your studies allow you to briefly glimpse pieces of the immediate future. You can not be surprised in combat and you use your Intelligence modifier instead of Dexterity when determining Initiative.
Quantum Leap
At 2nd level, you can create a temporal pocket to aid your movement. When you take the Dash action, you may step through a portal that causes time to stop around you, allowing you to move without fear of provoking opportunity attacks. To all outside viewers, you seem to teleport in space. During your movement, you can not interact with any item or creature other than yourself. You may use this feature a number of times equal to your Intelligence Modifier (Minimum 1) before requiring a long rest.
Divergent Reality
Starting at 6th, you become able to briefly see the possibilities of alternate timelines, catching glimpses of how your life could have gone differently. You gain proficiency in one tool, skill, or language of your choice, or you learn one cantrip from any spell list. During a long rest, you can exchange the proficiency or cantrip for another level. YOu use Intelligence as your spell casting modifier for and cantrip chosen by this feature.
Temporal Rewind
At 10th level, when a creature in sight makes an attack roll or saving throw, you are able to briefly rewind time. You may use your reaction to force an immediate reroll of the dice. You may choose to use this feature after the attack roll or saving throw has been rolled but before the DM announces the whether the roll succeed or fails. Once used, this feature requires a short rest to use again.
Dangerous Paradox
At 14th level, you gain the power and knowledge to send spells backwards through time. Your future self is capable of using you as a temporal anchor: a specific, isolated more within time around which spells can be created.
Gifts From The Future: As a free action, you may have a spell arrive from the future with no discernible source. This may occur on another creature's turn, as though an unseen caster had readied an action. Choose a spell of 1st to 5th level and a casting time of one action or bonus action from the wizard spell list. The effects of the spell occur with no action or component cost required, although you count as the caster of the spell for purposes of range, concentration, and ability scores.
Temporal Balance: Every effect requires a cause. When a spell arrives from the future, the temporal scales become unbalanced. After using the Gifts From the Future feature, you acquire a temporal debt: a promise that a spell will be cast backwards to rebalance the scales. While you have a temporal debt, you are unable to use the Gifts From the Future ability.
Repaying a Debt: During a short or long rest, you can perform an hour-long ritual to send the chosen spell into the past, thus paying off your debt. At the end of the ritual you cast the spell as normal, consuming material components and a spell slot of the correct level. The effects of the spell don't occur at the time of casting. If you don't have the ability to cast the spell, you have to prepare, learn, or otherwise acquire the spell before you can perform this ritual.
I get what your trying to say with divergent reality, but it says "you can exchange the proficiency or cantrip for another level" instead of "you can exchange the proficiency or cantrip for another" and there is a spelling mistake in the next sentence. Maybe remove the jumping through a portal for quantum leap, to leave it more vague to allow players to flavor it better.
Hope these suggestions help ;P
Dangerous Paradox is a very, very clever concept. I'd be willing to choose the school almost solely so I could play around with that.
Foresight and Temporal Rewind though... they seem to step a bit too much on the toes of the School of Divination.