Answer

When a player would exceed the 10-card limit for Feats and Items by gaining a new one, they may immediately discard any Feat or Item, including the one they just gained. This means:

• When you draw 2 Feats during the Build Phase and pick 1 to keep, if adding the chosen Feat would put you over the 10-card limit, you may choose to discard any Feat or Item you currently have, or the new one you just gained, to stay at or below the limit.
• You are allowed to see the new Feat before deciding which card to discard, so you can choose which to keep after seeing the new card.

This is supported by the following rule:

"If you would exceed the 10-card limit by gaining a new one, you may always discard any Feat or Item, even the one you just gained."
(page 13)

Summary

You only need to discard down to the 10-card limit after you have drawn and chosen the new Feat or Item, and you may choose which card(s) to discard after seeing the new one.

Source: page 13

Source: Core Rulebook (pp. 13, 15, 17, 35, 4)