Help Extract Animals from Red Tape Act of 2019 or the HEART Act of 2019 This bill modifies notice requirements in a civil forfeiture proceeding that involves the seizure of an animal involved in animal fighting. Specifically, the government must notify interested parties of an animal's seizure within 30 days (currently, 60 days). The notice period may be extended only if a delay is warranted after considering certain factors, including the cost to the government of providing shelter for the animal, the health of the animal and the effect of a delay on its rehabilitation, and any increased risk that a delay could necessitate the euthanasia of the animal. Additionally, the bill authorizes amounts in the Department of Justice Assets Forfeiture Fund to be used to pay for costs associated with a seized animal, including transportation, shelter, care, veterinary services, and humane euthanasia.