If Heedless Resurrection is used during combat on the enemy turn can I play the new card to a battlefield during combat

Yes, you can play the resurrected unit to the battlefield where the combat is taking place. According to RiftJudge FAQ #11033, the process works as follows:

Sequence of Events

1. Reaction: As a defender during combat, you play Heedless Resurrection as a [Reaction]. This opens a chain and sets the game state to Closed.
2. Cost: You kill a friendly unit at the battlefield to pay the additional cost. Although you may have removed your only unit there, you do not lose control of the battlefield because the game state is Closed while the spell is on the chain (Rule 187.4.c).
3. Resolution: Heedless Resurrection resolves. Because you still retain control of the battlefield, it remains a valid destination for the unit you are playing from your trash.
4. Entry: Once played, the new unit enters the battlefield. If the combat (showdown) is still ongoing, it will participate as a defender (Rule 459.2.b.4.a).

Important Constraints

• Targeting and Costs: You must follow standard targeting and cost rules: the unit you resurrect must be in your trash before you play Heedless Resurrection, and you cannot retroactively resurrect the unit you just killed to pay the cost (FAQ #9523, #11554).
• Cost Requirement: The resurrected unit must have an Energy and Power cost no greater than the unit you killed.

This interpretation is based on Rule 187.4.c and RiftJudge FAQ #11033.

Note: I could not fully verify the citation of Rule 357.2 regarding the cost constraint against the retrieved rules.