To Catch Up With, To Overtake, To Keep Up With
intransitive verb, godan verb
To follow then attach yourself to the whoever you're following is to catch up with someone.
おいつく
The readings are the ones you learned with the kanji, but you can also just notice that this word includes 追う and 付く combined.
あと五分くらいで追い付くと思う。
I think I'll catch up in about five minutes.
100メートル走でクリステンに追い付くことができたらオリンピックに出られるよ。
If you can catch up with Kristen in the hundred meter dash, you can compete in the Olympics.
まだちょっと気持ちが追い付いてないんです。
I'm still trying to catch up emotionally a bit.