There's precedent - William Cohen was a Republican Secretary of Defense for Bill Clinton.

Off-topic: That doesn't matter much since she vocally supported Hilary Clinton and also supports Joe Biden.

She spoke at this year's Democratic convention in support of Biden. Not saying that implies the potential for her to end up in his cabinet, but a lot of Republicans have crossed into independent or Democratic territory the last few years (some while retaining Republican party affiliation for now).