The short answer
Usually yes, provided you hold the rights and the programme does not require exclusivity — check the rules before submitting.
Most awards accept previously published work, since publication is evidence of quality rather than a conflict. Some programmes ask for first-publication rights or restrict entries that won another award in the same cycle.
Keep a record of where each project has appeared. If a programme requires exclusivity, entering anyway can disqualify the entry after the results are announced.
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