I have Reksai Breacher in base and play a unit not from hand. Is there a cost to accelerate the unit?

Yes, there is a cost to Accelerate the unit.

Even when Rek'Sai, Breacher grants the Accelerate keyword to a unit played from outside your hand, Accelerate is not free.

According to Rule 805.1.a and RiftJudge FAQ #9858, here is how it works:

1. Optional Additional Cost: Accelerate is an optional additional cost. It gives you the choice to have the unit enter the battlefield ready instead of its default state of exhausted.
2. The Cost: If you choose to use the Accelerate keyword to have the unit enter ready, you must pay [1] Energy and 1 Power as an additional cost.
3. Payment Timing: You must pay this cost during the "Pay Costs" step (Rule 357) of playing the card.
4. Power Type: Because most units played this way (or tokens affected by this) often have no domain or multiple domains, the Power portion can be paid with [A] (a Power of any domain).

In summary: If you want the unit to enter the battlefield ready, you must pay the 1 Energy and 1 Power. If you choose not to pay this cost, the unit will simply enter the battlefield exhausted.