New Game+

After clearing the game once, you'll be asked to save your cleared-game save file. Once you've loaded this file, proceed with the normal gameplay until you get to access your journal in your personal quarters. Here, you'll be able to access the additional options. Before discussing the new Journal options, here's the list of what is carried over to your New Game+ playthrough:

* The total Renown you’ve collected in the previous playthrough will be fully refunded to you.

* Saint Statue levels will be retained. You only need to further improve them.

* You won't be able to carry any items, money, weapons, accessories, or consumables from your last playthrough. However, all weapons that you can buy from the Armory is now available.

* All the Battalions you hired in the previous playthrough are already available. However, you still need to meet their Authority level requirement before you can assign them to your units.

* You can still get the consumable DLC items from your own bed.

* You'll get Crest Items based on the Crests of the characters you've recruited in your last playthrough. Simply placing them in a character's inventory (no need to equip) will allow that character to utilize the power of that crest item. See more details below.

Professor Level

This option allows you to spend renown to level up your professor level, based on the highest level you have attained in the previous playthrough. It will cost 4500 renown to reach A+. This should be take utmost priority before spending your renown to anything else. (unless you want to go through the hassle and limitations that comes along with low professor level).

Support Level

Support levels between you and all other characters have been reset. However, you can spend renown to “buy” the highest support levels you’ve attained with the said characters. This is very useful especially if you’re planning to recruit other students as early as possible. Since it costs 400 renown per support level, it’s more economical to at least do the normal means of building support (returning lost items, giving gifts, dining together, etc) to reach support level C then use renown to reach support level B. Upon reaching support level B with a student from another class, he/she will ask to join your class even if you haven’t reached their required stat or skill level.

Skill Levels

In this option, you can spend renown to “power-level” your way through skill levels. Since skill levels are tied to the classes you can certify to and weapons you can wield, you can easily reach the required skill levels without the need for faculty training or fighting. However, this should not be your first priority to spend renown on.

Class Abilities

This option allows you to buy the abilities and/or combat arts from class skills that you and your units have mastered in the previous playthrough. This option is quite useful for getting certain, powerful abilities like Byleth’s Enlightened One’s Sacred Power very early in the game.

Crest Items

You'll get Crest Items based on the crests of the characters you've recruited in your last playthrough. Simply placing them in a character's inventory will allow that character to utilize the power of that crest item(s). Since you don’t need to equip them as well, the user can still equip an accessory as normal. You can also buy additional Crest Items for 1000 renown each.

Crest Items are also perfect for enabling units with no crest to artificially have one or allow other units to equip and use Sacred Relics that are formerly exclusive to certain characters.

Since the activation rate for the Crest Abilities is not consistent, you should not focus your gameplay or setup around them. Bringing a crest practically takes up an inventory slot. Carrying two of them basically leaves you with only 4 inventory slots for your weapons, consumables, and accessory.

I can't confirm if placing a Crest item with the same effect as the user (like giving Marianne a Storm Dragon Sign) will stack the effects. However, you can have a crest-bearer carry a different crest item and have the chance to enjoy its effects. For units like Lysithea and Edelgard who both have two Crests by default, giving them additional crest items is like giving them additional crests.

Access to the Holy Tomb

You can now access to the Holy Tomb, where you can find Sothis as well. Similar to the Amiibo Gazebo where you can get free random items after scanning an Amiibo, you can also pick up better random items in the Holy Tomb, including stat-boosting items, accessories, and more. Visit it often whenever you explore.