“God seeks that which is pursued.” The meaning of this phrase is unclear and has given rise to many different interpretations. For example, because “pursued” is sometimes related to “persecuted,” one interpretation is basically that God seeks the persecuted in order to help them and hold their persecutors accountable. This divorces the last phrase of Ecclesiastes 3:15 from the first part of the verse and connects it to Ecclesiastes 3:16 which is about justice (cp. Duane Garrett, The New American Commentary). However, it seems like this is not likely because a phrase about God acting on behalf of the persecuted would more naturally come later, such as at the end of Ecclesiastes 3:16 or even 17.
Another interpretation is that the word “pursued” is related to the concept of pursuing, as in the phrase “pursuing the east wind” (Hos. 12:1, and cp. “herding the wind” in Ecclesiastes, REV) and thus the meaning is that God seeks and watches over the things that are “pursued,” i.e., the things that people have chased in vain but God is in charge of (C. Seow, The Anchor Yale Bible: Ecclesiastes).
A third interpretation is that God seeks that which has been “persecuted,” that is driven away or chased away, in this context meaning the things that are in the past and therefore no longer present—they have gone away. God seeks them with the intention of bringing them back, and this idea has led to translations such as “God will seek to do again what has occurred in the past” (NET; cp. R. Murphy, Word Biblical Commentary). The last two possible interpretations seem more likely than the first.