sustignuti

1. (+ acc.) to catch up with
   Trčao je brže i sustigao ga pred ciljem. — He ran faster and caught up with him before the finish line.
2. (in development, level) to catch up with; to draw level with
   Srbija još nije sustigla razvijene zemlje. — Serbia hasn't yet caught up with the developed countries.
3. (of the past, consequences) to catch up with
   Na kraju ga je sustigla prošlost. — In the end his past caught up with him.

The variant sustići is more common and means the same.