This would require a constitutional amendment. Article V makes Congress a participant in the formulation of amendments. The president is not a participant in this process.
He could go as a delegate from New York.
Here is the way I see term limits working. Say I, NCC-1701, want to run for a position on The Hill. I win. I have, say, 12 years maximum and the clock is running. That means I could have two Senate terms, six House terms or any combination thereof. After my 12 years THAT’S IT! I can’t lay off a cycle and run for another 12 years max. No, my time is up. Whatever I had wanted to do in that time is over. Go home and find another job.
Oh, piff.
Trump has two of the most essential and useful tools...a bully pulpit and no fear in it's use.
See: Reagan, Ronald.