strive after (something)
To put forth a great and tenacious effort to attain or accomplish something, especially that which is uncertain or intangible. I have spent my career as an artist striving after beauty and truth in their most ideal forms. You should spend less time striving after the praise and acceptance of others.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
strive after something
to try very hard to obtain something. I am always striving after perfection. Ted was striving after a promotion and finally got it.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.