so azir sovereign accelrate would cost 4, and you must recycle 1 body rune to accelerate correct?

Almost — the base cost of 4 Energy is right, but the Accelerate power isn't Body.

Azir, Sovereign is an Order unit, so his Accelerate is "pay [1] + 1 Order Power as an additional cost." The Power portion must match one of the unit's domains (Rule 805.1.a.1), so you need to recycle an Order rune, not Body. Total: exhaust 5 runes (4 base + 1 for the Accelerate Energy) and recycle 1 of them if it's an Order rune — the same rune you exhausted can be the one you recycle.

If Azir had no domain, that power would become [A] (any domain), but he's Order, so it doesn't.