1. To dispatch a request for someone or something to appear or be brought (to one). We'll need to send after some replacement parts to get this thing working again. A: "Quick, someone fetch the doctor!" B: "We've already sent after him!"

2. To direct someone to pursue or bring back someone or something. In this usage, a noun or pronoun is used between "send" and "after." When Mary suddenly stormed off in a huff, I sent Susan after her to make sure she was all right. I'll need to send Tom after some more lumber if we're going to get this shed finished.