I believe that Boyan Slat and The Ocean Cleanup are leading the way on solving this.
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Boyan Slat, Ocean Cleanup founder, wrote an opinion piece on plastic pollution a few days ago. He says, among other things, ~~that his effort won't solve plastic pollution~~ plastic leakage will increase if we keep increasing plastic production.
Producing less plastic is the way to solve this. Cleanup operations can then help bring the remaining plastic pollution further down to less-hazarbous levels.
Edit: Correction on Boyan Slat's claim. He actually say we should assume plastic production will keep growing, so cleanup would be needed. But I doubt cleanup efforts would be enough if plastic production (and leakage) continuously increase. They can however give us more time to reduce plastic usage.