To go in search or quest of; to look for; to search for by going from place to place. The man asked him, saying, what seekest thou? And he said, I seek my brethen. Gen. 37. 2. To inquire for; to ask for; to solicit; to endeavor to find or gain by any means. The young lions roar after their prey, and seek their meat from God. Ps. 104.

(a) to seek, to seek for," e.g., Matthew 7:7 - Matthew 7:8; Matthew 13:45; Luke 24:5; John 6:24; of plotting against a person's life, Matthew 2:20; Acts 21:31; Romans 11:3; metaphorically, to "seek" by thinking, to "seek" how to do something, or what to obtain, e.g., Mark 11:18; Luke 12:29; to "seek" to ascertain a meaning, John 16:19, "do ye inquire;" to "seek" God, Acts 17:27, RV; Romans 10:20;

To seek out, properly implies to look for a specific thing among a number. But in general, the use of out and after with seek, is unnecessary and inelegant. To seek God, his name, or his face, in Scripture, to ask for his favor, direction and assistance.