に追いつくだろう

will catch up with

→ に
phrase Rare #24,245
will catch up with The に marks the person or thing being caught up to, while だろう indicates a prediction or likelihood. The phrase can also mean “will probably catch up with.”
JA: 急げば、電車に追いつくだろう。
EN: If you hurry, you'll catch up with the train.

彼は一時間で我々に追いつくだろう

He’ll catch up with us in an hour.

もし急げばあなたはに追いつくだろう

If you hurry, you'll catch up with him.

私はすぐにあなたに追いつくだろう

I’ll catch up with you soon.