So yeah started campaign with siblings with me being the dungeon master this time

long story short sibling manage to tame a wolf and she wants to keep as a companion

actually dont mind and if makes campaign more enjoyable sure i let her keep the wolf she tamed...just need some advice on some mechanics i can implement to still make the campaign fair, challenging a bit and fun...and make the wolf fair in battle

...like are there a list of feats for tamed beasts/animals in DnD?

if she is a Ranger and a beast master, she can have this: https://www.dndbeyond.com/sources/tcoe/ranger#BeastMasterCompanions

Volo's, if you had it, has a section: https://www.dndbeyond.com/sources/vgtm/monster-lore#AlliesMinionsandPets

I think you talk with the player and explain, at low levels, the wolf can be solid, but at higher levels, it will die, quickly. 
So they should make a choice. Do they want the wolf to help them overcome challenges, in and out of combat or no. Then you make a deal, if they use the wolf to help, it’s fair game. Enemies will attack it, fireballs will kill it, you have to figure out how it’s climbing that ladder, explain to the innkeeper why they should allow a wild animal in the building, etc.

But, if they just want it as a pet, for role play, then it’s all but immortal. It can’t help the party, but it also can’t be hurt, and will happily tag along.

If they want it to help and be a combatant, you might look at the sidekick rules for a way to let it be useful, without stealing the show. 

Quote from Xalthu >>

I think you talk with the player and explain, at low levels, the wolf can be solid, but at higher levels, it will die, quickly. 
So they should make a choice. Do they want the wolf to help them overcome challenges, in and out of combat or no. Then you make a deal, if they use the wolf to help, it’s fair game. Enemies will attack it, fireballs will kill it, you have to figure out how it’s climbing that ladder, explain to the innkeeper why they should allow a wild animal in the building, etc.

But, if they just want it as a pet, for role play, then it’s all but immortal. It can’t help the party, but it also can’t be hurt, and will happily tag along.

If they want it to help and be a combatant, you might look at the sidekick rules for a way to let it be useful, without stealing the show. 

This is a really good piece of advice.

You could also use the sidekick rules in Tasha's to turn the wolf into a sidekick. It will allow the wolf to grow with them and remain useful to the party for a longer period of time. 

Yeah, I would go the sidekick rout, or if you don’t have access to Tasha’s email hen just give it levels as a Champion fighter, it’s pretty much the same thing more or less.

As an initially wild animal if you are going to give it levels you might want to check snider ranger levels rather than fighter. Because of things like the fighting styles and ranger magic the sidekick rules are better. As a leveled entity you probably want to keep a level below the party so it is a help but not a lead. As for magic, there are spells at each level (at least1) that could be interpreted to be naturally developed talents usable only a limited number of times a day. It wouldn’t have full ranger functionality but then it’s not supposed to be a lead only an assist.

Since this is D&D, we can hand-wave some things. I would turn the wolf into a Familiar. Maybe...

Some NPC has a plan to do "something". He cast Find Familiar for to support that plan, but then the Party came along and scooped up the Familiar. The NPC could have dismissed the familiar and gotten back on track, but he was interested in the Party and let them keep the Familiar for a while to see how things played out. After some amount of time, he meets the Party (for either good or ill purposes) and because they love the Familiar so much, he teaches them the Magic Initiate feat so they can then "own" the familiar going forward.

This solves the problem of the pet dying and lets the Party keep their beloved pet.

Good luck!