There are 4 potential people who could end up fighting Akainu:
Blackbeard is a very ambitious man and in order to establish his clout in the One Piece world he has to show some kind of exploitation. Though he got to the epithet of Yonko after beating remnants of Whitebeard Pirates including all the commanders except for Ace, but that doesn’t tantamount to the league of other Yonkos.
Blackbeard have to show some exploit to the world in order to let the people think that he is more of a big shot than his current status and invading Baltigo was the fruition of that thought.
In the end he is gonna challenge Marine and Akainu. When he was fleeing to the New World with his newly recruited crew, he saw Akainu coming but he didn’t go for a clash even though he had the entire crew with him though he was showing off in Marineford and proclaiming himself as the strongest man alive; when he saw Akainu he said: “we are not ready yet to fight him,” which means he has planned to fight him eventually.
#2-MONKEY D. DRAGON
Akainu is kind of infatuated with Dragon. The only reason he pursued to finish off Luffy in Marineford was the very fact that he was Monkey D. Dragon’s son though you can argue that Luffy’s gust of Conqueror’s Haki played a role, regardless being Dragon’s son played the most significant role in his judgment. This only intimates that they have a history though we are in a total dark regarding the possible contentions between them.
Who knows Dragon may have betrayed Marines/World Government while pretending faithful to Akainu the whole time and it may have scared him to such extent that he began to loathe Dragon to his very core.