It all depends on one factor - can you shoehorn your new API into your old one? If you can, then augment the calls to the old parser's functions with simultaneous calls to the new parser's functions. Then, when you're happy, remove the old parser code and let the old parser functions map to the new parser's functions.

Then, you do two more things:

1. New development goes against the new parser
2. Maintenance of old development includes changing calls from the old parser to the new parser.

Eventually, you remove all references to the old parser and then you remove it. Usually takes between 6-24 months.

Now, if you can't shoehorn the calls ... well, good luck.