A Master Falconer is a ranger whose practice of the art of falconry goes beyond the mere skill of training, tending, and hunting with raptors or other birds of prey.  Whether they started out as a falconry hunter for a noble household, learned the art on their own or were in some sort of military force, at some point they formed a relationship with one special bird, gaining an almost intuitive understanding of its nature, moods, and even thoughts.  As long as the Falconer has their special bird companion with them or at least is in regular contact with it,  the two of them can operate in the closest of harmony to accomplish things impossible for an ordinary falconer.  Through their relationship to their special companion, they also gain a closer understanding of the minds and spirits of other birds of prey, giving them an advantage over other falconers in dealing with such creatures.

Avian companion

The master falconer forms a special relationship with a single bird, who will respond with great loyalty and devotion.  The falconer comes to understand this bird on a deep level, knowing instinctively its strengths and weaknesses, how it will respond to a given situation, and the best way to communicate with it and have it do what the falconer asks; they even gain a basic understanding of what the bird is thinking.  This bird always has the maximum number of hit points for its hit dice,  plus 3; and gains 3 more each time the ranger gains a level.

Blood hawk

Your avian companion is a blood hawk.  This bird always has the maximum number of hit points for its hit dice, plus 3; and gains 3 more each time the ranger gains a level; otherwise, use standard stats.

Eagle

Your avian companion is an eagle.  This bird always has the maximum number of hit points for its hit dice, plus 3; and gains 3 more each time the ranger gains a level; otherwise, use standard stats.

Hawk

Your avian companion is a hawk. This bird always has the maximum number of hit points for its hit dice, plus 3; and gains 3 more each time the ranger gains a level; otherwise, use standard stats.

Owl

Your avian companion is an owl. This bird always has the maximum number of hit points for its hit dice, plus 3; and gains 3 more each time the ranger gains a level; otherwise, use standard stats.

Valenar hawk

Your avian companion is a Valenar hawk. This bird always has the maximum number of hit points for its hit dice, plus 3; and gains 3 more each time the ranger gains a level; otherwise, use standard stats.

Vulture

Your avian companion is a vulture. This bird always has the maximum number of hit points for its hit dice, plus 3; and gains 3 more each time the ranger gains a level; otherwise, use standard stats.

Intuitive understanding

Because of the intimacy of their relationship with their bird companion, the ranger also gains an intuitive understanding of the minds and lives of other birds of prey.  When handling any trained bird of prey other than their bird companion, they gain +4 to their Animal Handling roll, and also get +3 to their Charisma when determining how wild birds of prey respond to them.

Aid in combat

By taking advantage of their natural inclination and training to swoop down and attack prey, the ranger can command their bird companion to attack a specific enemy on the battlefield.  They must have worked with their companion for at least a month to teach it signals by which the ranger indicates what s/he wants the bird to do.  The bird must be able to see and/or hear the ranger for this communication to take place.  If the ranger concentrates, s/he can coordinate his/her attacks with the bird's on a single enemy.  The ranger loses the ability to fight with two weapons, if they had such training, and cannot cast spells while they are coordinating attacks; but while they are doing this, the ranger and their bird companion always attack with advantage and impose disadvantage on the enemy's attacks.  By the time the ranger has reached 7th level, they are skilled enough in this coordinated fighting to also gain +1 to hit and damage for themselves and their bird companion, and correspondingly impose a -1 penalty to the enemy's to hit and damage; another +1/-1 is gained at 15th level.

Deep understanding

By 7th level, the Master Falconer and their bird have been together so long that they have gained an intuitive understanding of each other's minds.  Their mutual comprehension is such that communication at the level a speak with animals spell grants is always possible between them, at will; but no spell is involved, nor are words necessarily involved.  The ranger and bird interpret each other's gestures and body language, nonverbal vocalizations, and other such signs.  They must still be able to see and hear each other, and distractions such as being in combat can limit the amount of detail that can be communicated.

Psychic bond

By 11th level, the bond between the ranger and their bird companion is such that their minds are, in a sense, linked.  The ranger can sense their companion's emotions and state of health as long as the bird is within one mile of them.  If it is within half a mile, the ranger can concentrate on it once per short rest in order to share the bird's perceptions and senses; this concentration is so demanding that the ranger can do nothing else during this time and can only maintain it for a number of minutes equal to their Intelligence score.  If anything occurs to them during this time that would break the concentration of a spellcaster, they must make an immediate Intelligence check to maintain their link with their companion; if they take actual damage, the check is made with disadvantage.

Linked souls

By 15th level, the bond between the ranger and their bird companion is so deep that in some senses it can be said that they share part of their souls.  Three times per long rest they can each gain some of the special characteristics of the other.  Specifically, the bird can gain the ranger's bonuses against their favored enemies, gain the same primeval awareness of the surrounding area that the ranger has, or add the ranger's Ability bonuses to their own actions; and the ranger can gain the ability to fly at the speed and maneuverability of their bird companion for a number of minutes equal to the sum of their Strength and Constitution, sharpen their own senses to the level of their bird companion's, or add damage to a single unarmed attack identical to that dealt by their bird companion's talons.  In addition, their bond is so deep that once per week, if one of them is brought to 0 hit points the other can sacrifice up to three of their own hit points which are added to the wounded one's total.