I'm spinning up a new campaign set in the Forgotten Realms, and a new player (having never played a TTRPG before) wanted a slightly different background for his Dwarf Barbarian; something that reflected his IRL care for green places and that knit together nicely with the character's backstory. We started by messing a little with the Farmer background from the 2024 Player's Handbook, but I increasingly felt it deserved more, so I spent some time drafting this new background for both the 2014 and 2024 rules.

The Forester is here for you if you want a character deeply entwined with the forests of your world and will suit any campaign where there are green places needing care and protection. It includes a background-specific weapon—the Forester's Axe—also detailed below.

Forester

You grew up tending the forests near your home, ensuring their health and wellbeing, and protecting the sacred places within—glades, springs, and the like. Your role has also included harvesting timber for construction and toolmaking in your community in harmony with the needs of sustaining the forest by taking only trees whose lives were ending, or younger timber the loss of which would not affect the forest negatively. You have learned to understand the dryads and other fey denizens of the forest in order to negotiate the harvesting of the right trees.

5e/2014

Skill Proficiencies: Nature, Survival
Tool Proficiencies: Woodcarver's Tools
Languages: Sylvan in addition to any others you have
Equipment: Woodcarver’s Tools, Forester's Axe (see below), Dagger, Bedroll, Backpack, Pouch, Tinderbox, Rations (3 days’ worth), Rope, Traveler’s Clothes, Waterskin, 20 GP

Feature: Respect of the Forest Folk

Spending years in the forest, carefully and respectfully selecting just the right trees both for their use after felling, and so that their removal does not upset the balance of the woodland, has brought you the respect of those who dwell in the green.
You are able to communicate with all humanoid creatures of the forest with a basic sign language, and with the fey directly by speaking their language.
Should you become lost or incapacitated in a forest environment, you will be given guidance to safety by the creatures that live there. The form of that guidance may be direct or indirect.

Suggested Characteristics

Use the tables for the outlander background in the Player’s Handbook as the basis for your traits and motivations, modifying the entries when appropriate to suit your identity as a member of your community.
You have spent a large portion of your life so far in the forest, and deeply respect those places to the extent you consider the features of the woods—glades, springs, and such—as sacred. You may worship a forest spirit rather than one of the more well-known gods. You will never fell a living tree without first negotiating with those that live in the forest.
Your reasons for leaving the woods and seeking a life of adventure may vary widely; was it some sort of upheaval, a change in your community, a desire to seek greater knowledge of the great forests that cover other lands, or a wish to understand the particular magic of green places?

5.5e/2024

Ability Scores: Strength, Wisdom, Constitution
Feat: Tough or Alert or Forest Dweller (An Equal Portion Dealt, p9, Keith Ammann)
Skill Proficiencies: Nature and Survival
Tool Proficiencies: Woodcarver's Tools
Equipment: Choose A or B: (A) Woodcarver’s Tools, Forester's Axe (see below), Dagger, Bedroll, Backpack, Pouch, Tinderbox, Rations (3 days’ worth), Rope, Traveler’s Clothes, Waterskin, 20 GP; or (B) 50 GP

Forester's Axe

The Forester's Axe is a single-bladed variant of the Battleaxe designed specifically for felling trees, though also usable as a weapon. It has a contoured, smooth handle that facilitates a swing that will drive the blade deep into timber or armour.
Type: Martial Melee Weapon 
Cost: 10 GP 
Weight: 4 lbs

Proficiency with a Forester's Axe allows you to add your proficiency bonus to the attack roll for any attack you make with it.

This weapon has the following mastery property. To use this property, you must have a feature that lets you use it.

Topple. If you hit a creature with this weapon, you can force the creature to make a Constitution saving throw (DC 8 plus the ability modifier used to make the attack roll and your Proficiency Bonus). On a failed save, the creature has the Prone condition.