With the update for New Light, due to feedback that it was difficult to differentiate between Bounties and Pursuits in the Pursuits tab since everything was all together, Bungie updated the Pursuits tab to be displayed differently. Previously, the Pursuits tab had 3 pages of 21 items each (for a total of 63 items). Both Bounties and Pursuits were mixed up in that list. With the update, those 63 items were split up between the Pursuits section (now named Quests) and the Bounties section. Along with that, the Pursuits tab was renamed to Quests. The same 63-item limit still applies, so you can only have a total of 63 combined items between your Quests and your Bounties. So, even if your Bounties section appears to not be full because there are more visual boxes for Bounties to go into, you still cannot gain more if you're at the max of 63 items. You can see the total number of combined items you have at the bottom left, as ishikusui mentioned in the other reply. In order to pick up more, you'll need to either finish or abandon some that you already have to free up space. I personally don't recommend abandoning any Quests as it may cause problems down the line if there's a bug or issue.