So....two answers here.
Non-Adventurer's League Play
It is entirely and completely up to the DM. There are no rules that cover this.
The PHB only talks about how PC Death can happen. The DMG makes only two mentions of PC Death...
Your campaign might allow player characters to take on lower-level NPCs as followers. For example, a paladin might have a 1st-level paladin as a squire, a wizard might accept a 2nd-level wizard as an apprentice, a cleric might choose (or be assigned) a 3rd-level cleric as an acolyte, and a bard might take on a 4th-level bard as an understudy.
One advantage of allowing lower-level characters to join the party is that players have backup characters if their main characters take time off, retire, or die. One disadvantage is that you and your players have more party members to account for.
Emphasis Mine from DMG p92
Then also has suggestions on p236 that a small group may want to keep some back-up characters around in case their character dies...
Multiple characters can be a good idea in a game that features nonstop peril and a high rate of character death. If your group agrees to the premise, have each player keep one or two additional characters on hand, ready to jump in whenever the current character dies. Each time the main character gains a level, the backup characters do as well.
These two quotes are both suggestions, not rules, and do not answer definitively how you should handle a replacement character's level. The first quote implies you would be handing a PC a lower level 'follower' to take over as their new PC...while the other implies that they would have a same-level replacement character waiting in the wings.
Volo's, Xanathar's, Mordenkainen's, or any of the adventures make no further mention of it
Level 1. If you can't get yourself Raised.
If an AL Character dies and the party cannot resurrect them on-the-spot, here are their options:
- Create a new 1st Level character
- Assuming their corpse can be toted back to civilization and is in good enough shape for the spell to work, the player may spend 1,250gp to pay for a Raise Dead to happen off-screen. Optionally, the party may chip in to help pay for this.
- If a character is between level 1 and 4, and is part of a Faction, they may draw on Faction Charity for a free Raise Dead, though doing so forfeits all XP and Rewards earned during that session (including any earned prior to the character's death.
The above is drawn from the AL Tyranny of Dragons Player's Guide, and has been repeated in each player's guide since.