Assuming the decedent didn't give away at least $4.7MM in tax free gifts during her lifetime, then there will be no tax due
As with all advice posted on a public forum, my advice is not to be relied upon. Given the limited set of facts provided in the question, and the limited amount of research conducted in my answer, my advice is not intended to constitute "legal advice," and you should consult with another tax attorney or CPA to get a dependable answer to your question
There will be income tax on the annuity payments, its due from the recipient (on the amount in excess of the the cost of the annuity). Mr Ayar correctly pointed out that there is no estate tax unless taxable gifts and the net value of the estate total in excess of 5.25mm dollars.