I play Heedless Resurrection, killing my Elder Dragon. Can I then play the same Elder Dragon I just killed?

No, you cannot use Heedless Resurrection to kill your Elder Dragon and then immediately play that same Elder Dragon from your trash.

According to RiftJudge FAQ #9523 and Rule 355.15, the target for Heedless Resurrection must be chosen and locked in during Step 2 of the process of play, before you pay the costs in Step 4. Because your Elder Dragon is still on the board at the time you choose your target, it is not yet in your trash and is therefore not a valid target.

Sequence of Events:

1. Play the Spell: You announce Heedless Resurrection and place it on the chain.
2. Make Choices: You must choose a valid unit from your trash to be resurrected. At this moment, your Elder Dragon is still on the board and is not a valid target.
3. Lock Targets: Your target selection is now locked in.
4. Pay Costs: You pay the additional cost by killing your friendly Elder Dragon, moving it to the trash.
5. Resolution: You resolve the spell, but because your target was already locked in during Step 2, you cannot retroactively choose the Elder Dragon that just arrived in the trash.

Sources: RiftJudge FAQs #9523, #10168, and #10194.