Sar Shalom

Ps. 34:14
Depart from evil and do good;
seek peace, and pursue it.

This is a stark contrast from the meek and mild "Oh, I've just got to be patient and maybe one day peace will fall into my lap if God decides to give it to me." Yes, peace is a gift. But we are meant to seek it, to pursue it, not just wait for it with a gnashing of teeth until it gets there.
Pursue: "radaph" - to run after
Seek: "baqash" - to search out, to strive after, to request. specifically used in worship or prayer.

How? Doesn't it seem like an oxymoron to fervently look for and run after peace?

Yes, if by peace you mean sheer comfort.

No, if you consider that Jesus is Sar Shalom*, Prince of Peace. "Sar" implies rulership and governance, from a verb that means to have dominion. Jesus isn't just the sub-ruler (like we think of "prince"), nor is He just excessively anti-confrontational ("the best at peace"). Peace is His to bestow, and it's His to control.

Peace isn't found in things being calmed or solved or made clear - it's found the Prince. And found more abundantly if we run towards Him, rather than away from Him, if we seek to spend time with Him rather than figuring out our lives and making ourselves secure, rather than sitting and waiting and twiddling our thumbs for peace and letting anxiety build and fester inside. Peace isn't denying that things are out of (our) control, nor is it succumbing to the 'whelming flood. Any peace that you get without coming to the Prince won't last, really.

^Above were things God showed me one night when I was being anxious over career stuff and whether or not teaching was really right. And you know what? It's great that I have so many options, but no single one is "right". Which career I choose is not crucial, so long as I glorify God in what I do. And I feel that teaching is one arena where I can definitely do that while growing in Him as well. And that peace...was found when I stopped worrying and let Sar Shalom take care of it.

*my Hebrew grammar is probably poor and these words may be in the wrong order.