I don't think any of the earth's remaining sentient species (cetaceans, primates, elephants, cephalopods etc.) would take over in any way that would resemble how humans have dominated the earth (I won't go into the negative aspects of that domination at this time).
I think either viruses or bacteria would become the dominant species on the planet, because we'd no longer be here squirting anti-bacterial soap on every surface of our lives.
I think insects would be a close contender to the throne.