Hopefully, with this homebrew, gone are the days of not being able to take an action because: "Walk five feat! Bite boy! Bite again I guess! Bonus walk back fast!" I mean really. In reality with animal training an animal will follow basic commands, but still has a brain. The people giving said commands usually work with the animal rather than standing around ordering it. Also, most of those commands will, by D&D standards, be multiple actions or even a directive (meaning a action or even a series of actions that will be carried out until given another order). My issue here with the original subclass is not the damage output, but how lame the class is once you read the fine print. I actually think it is kinda silly to expect damage output from your animal companion. Again if we look at reality animals are used for utility not to replace our weapons (though they still bite), and so without further pause my ranger beast master:

Tamer’s Companion

At 3rd level, you gain a beast companion that accompanies you on your adventures and is trained to fight alongside you. Choose a beast that is no larger than Medium and that has a challenge rating of 1/4 or lower. Add your proficiency bonus to the beast’s AC, attack rolls, and damage rolls, as well as to any saving throws and skills it is proficient in. Its hit point maximum equals the hit point number in its stat block or four times your ranger level, whichever is higher. Like any creature, it can spend Hit Dice during a short rest to regain hit points.

Your companion obeys your commands and takes its turn on your initiative directly after you. On your turn, you can issue the move command to your animal companion (no action required by you) or  give it a directive as an action; you may also commands to take the Dash, Disengage, or Help action. If you don't issue a command, the beast takes the Dodge action.

If you are incapacitated or absent, the beast acts on its own, focusing on protecting you and itself. The beast never requires your command to use its reaction, such as when making an opportunity attack.

While traveling through your favored terrain with only the beast, you can move stealthily at a normal pace.

If the beast dies, you can obtain a new companion by spending 8 hours magically bonding with a beast that isn’t hostile to you and that meets the requirements.

Companion Directives

Beginning at 3rd level, on any of your turns you may issue a brief command or directive as an action or as your extra attack when using the [Tooltip Not Found] action. While out of combat your companion will do its best to follow your commands. In combat you may only use the basic commands or one of following directives that it is well trained in.

Protect:

Given the command to protect, your companion will put itself between you, or an ally you designate, and the enemy. If an enemy approaches it will begin barking, growling, hissing, or something similar, loudly (as a free action). While the directive is active it may make an opportunity attack when someone approaches its melee range. If it has not moved during your last turn it may move up to half its movement speed when your opponent moves.

Hunt:

Given the command to hunt, your companion will use whatever sense is the keenest to use. It must be given a scent or something similar to track.  You may add your animal companions wisdom modifier (doubled if it has keen senses) to your survival check to track someone or something.

Attack:

Given the command to attack, your companion will attack an opponent each turn until directed otherwise.

Hold:

Given the command to hold, your companion will grapple an opponent, if physically possible. It will release the target on your command or if it sustains a critical or if it is at 5 hit points or lower.  If it cannot grapple the creature then it will harry it instead (example: an eagle may claw, nip, or beat with its wings repeatedly) giving advantage on attacks against that creature, but not impairing its move speed.

Retrieve:

Given the command to retrieve your companion will attempt to bring you an object or willing creature if it can be carried. If the object is on a hostile creatures person then it may attempt to pick pocket (Dexterity: sleight of hand) or Disarm an opponent (see DMG disarm), both will provoke an opportunity attack. It will be unsuccessful regardless of rolls if the opportunity attack lands.

Rigorous Training

Beginning at 7th level, your animal companion's attacks now count as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.

In addition, you have worked to bring out the best in your animal companion. You have learned special techniques that you can use in tandem with your companion by magically linking with them. You can expend a spell slot to activate one of the following a number of times equal to the level of the spell slot expended; doing so ends any directive given.

Pack Hunting:

If your animal companion has pack tactics you may utilize this ability. Before you take your action, when you and your animal companion are in melee range of an enemy, your animal companion may attack. If the attack hits then you may use your reaction to make a melee attack with advantage against that enemy. If your reactionary attack hits, you animal companion may use its reaction to attack that enemy with advantage. When using this ability, your animal companion's attacks count as your attacks for the purpose of hunters mark.

Bird's Eye View:

If your animal companion has a flying speed you may utilize this ability. Your animal companion sores high in the sky delivering intelligence from above. You gain an extra reaction. All ranged attacks have advantage. Any hostile creature attempting to stealth without a structure or large aerial obstruction has disadvantage.

Primal Bond

Starting at 11th level, you gain the traits of your animal companion.

Share Spells

Beginning at 15th level, when you cast a spell targeting yourself, you can also affect your beast companion with the spell if the beast is within 30 feet of you.