Extend or go beyond a promise

JLG's and Billy Moon's answers are spot on. I'd add two things:

• Your thesis does not contribute to fulfilling the promise, which was fulfilled before you were admitted; it contributes to fulfilling something else.
• Fulfill is a very potent word, and it defeats its potency to employ it in a context where it is merely a stepping stone toward something else. It's like (I date myself) bringing in the Beatles to open for the Monkees. Save it.

I'd go for something more like:

Many years ago I made a promise to my late maternal grandmother that I would do my best to get admitted to a university. I made good on that promise; I hope this effort justifies her insistence and contributes to fulfilling the larger dream she had for me.

An idiom that might suit this situation is that you went above and beyond.

I hope this effort goes above and beyond fulfilling that promise.

Fulfill is an absolute, so can not be extended. You might however, fulfill a promise, surpassing all expectations. You might also more than fulfill a promise, which in itself implies the promise has been fulfilled.

p.s. congratulations