No mine were all almost fully grown at 2.5 years even the connie who should make 14.2 finished at 142cm and didnnt grow after her grading which was carried out at 3 and was 142 when measured for her workers classes
What’s her breeding? Was she a late/early foal at all? Some breeds mature slower than others but personally I doubt she’ll make 15hh if she’s 13.2hh at three.
At 3 they are pretty much done. I know people say their horses grew 3 hands at 6 but it doesnt happen often, and those that do tend to come up through the wither rather than a lot of all over growth. The growth plates are closed for limbs etc in a 3yr old.
I have one who went from 14.1hh at 3 to 16hh at 5, but she was very weedy and underdeveloped at rising 3. My other two horses grew 1 inch and zero inches after turning 3.
I'd think she's unlikely to make much more than 14h unless she's really backward in her development. My current pony was 13.2 1/2 at 3 and is now 14.0h at 6 and that is pretty usual growth.
Have you seen the filly's parents?