In the film Jurassic World we see the mosasaurus jump out of the water to catch a pteranodon as well as beaching itself to catch the i-Rex™.
Presumably it can simply keep doing that whenever it gets hungry. There's apparently no shortage of dinos (both flying and non) left on the island at the end of the film.
Colin Trevorow seems to have confirmed this idea in a podcast interview with Empire Magazine
Empire: The mosasaurus. I have to ask, what has it been eating, because this movie is set like four or five years….
CT: Well, but the opening sequence is set just after, there’s three years that pass. We didn’t put that type up onto the screen but the opening sequence could even be weeks after or a few months after. And then time passes to allow them to create that creature
Empire: I was trying to work out if the mosasaurus was jumping up and eating birds...
CT: Probably some. I think if some nesting pteranadons were on the water and if an animal came down to drink and didn’t realise it was salt-water, they’re in trouble
Jurassic World Fallen Kingdom Spoiler Special ft. J.A. Bayona & Colin Trevorrow