The actual wording of the sentence in question is this:
Is there anything that you would recommend that somebody in the future that they do differently if they were overseeing this kind of pandemic response?
The gist of this question might be stated as follows:
Is there anything that you would recommend that somebody who was responsible for overseeing this kind of pandemic response in the future do differently?
In current English usage, construing "they" as a singular pronoun when its referent is a singular noun or pronoun is more or less standard. In this case, as Xanne notes in an earlier answer, "somebody" is the referent for "they." In turn, "somebody" refers to a hypothetical person engaged in executing or reviewing a response to a future pandemic.
The repetition of "that they" after the phrase "that somebody in the future" is syntactically superfluous, as "that they" merely repeats the idea contained in the earlier words "that somebody." This kind of verbal stumble—or repetitive emphasis, as the case may be—is extremely common in speech, and listeners quickly learn to filter out (almost unconsciously) such excess verbiage in making sense of what a speaker is saying.
The word overseeing is a bit of an umbrella term here, as it can encompass both executing a policy and examining how a policy has been executed. To complicate the situation further, the question is presumably being asked by someone engaged in oversight not for the purpose of enforcing a policy or merely assessing it afterward, but for the purpose of formulating a new policy or revising an existing one to be put into practice and supervised by others.
As Xanne points out, the conditional form "if they were overseeing" is appropriate here because the speaker is referring to a hypothetical future situation in which the "somebody" in question had ongoing oversight responsibilities, not a situation where the person had overseen policy in the past but was no longer overseeing it.
