We found one dictionary that defines the word run up to:

Phrases: run up to someone, more... ▸ Words similar to run up to ▸ Usage examples for run up to ▸ Idioms related to run up to ▸ Wikipedia articles (New!) ▸ Words that often appear near run up to ▸ Rhymes of run up to ▸ Invented words related to run up to