search after (someone or something)
To try to locate or endeavor to obtain someone or something. We've been searching after a new HR manager, but so far the none of the candidates have been the right fit. I'm searching after a computer that can render a lot of complex 3D models.
search after someone or something
to look for someone or something. (Perhaps over a long period of time.) We searched after a suitable candidate for weeks. I am searching after a part for my '57 Chevy.