
auf jemanden/etwas zukommen
to approach
To approach a person or thing; to move in their direction.
Ich sah, wie eine dunkle Wolkenfront auf uns zukam.
I saw a dark front of clouds approaching us.
to approach / to be due
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to approach
To approach a person or thing; to move in their direction.
Ich sah, wie eine dunkle Wolkenfront auf uns zukam.
I saw a dark front of clouds approaching us.

to be coming
Describes an event, task, or challenge that lies ahead in the future.
Mit dem neuen Projekt wird eine Menge Arbeit auf uns zukommen.
With the new project, a lot of work will be coming our way.

to send someone something
To send, transmit, or give something to someone, often through formal channels.
Wir werden Ihnen die Vertragsunterlagen nächste Woche zukommen lassen.
We will send you the contract documents next week.

to be due to someone
To be due to someone or belong to them by right; to be appropriate for someone.
Dem Sieger kommt die Ehre zu, die Trophäe als Erster zu heben.
The winner is due the honor of being the first to lift the trophy.
'Zukommen' is a separable verb. In a main clause, the prefix 'zu' goes at the end. In a subordinate clause or in an infinitive construction, the verb stays together.
Eine große Aufgabe kommt auf dich zu.
A major task is coming your way.
In the meaning 'sich nähern' (to approach), 'zukommen' is almost always used with the preposition 'auf' and the accusative. So the structure is: 'auf jemanden/etwas zukommen' (to approach someone/something).
Der Läufer kam langsam auf die Ziellinie zu.
The runner slowly approached the finish line.
You distinguish the literal meaning (m01) from the figurative meaning (m02) through the subject. If a concrete object is moving, the meaning is literal ('ein Auto kommt zu' — a car is approaching). If the subject is abstract ('Arbeit' (work), 'Kosten' (costs)), it is figurative.
Pass auf, da kommt ein Fahrrad auf dich zu!
Watch out, there's a bike coming toward you!
The phrase 'jemandem etwas zukommen lassen' is a fixed, formal expression for 'jemandem etwas schicken' (to send someone something). The recipient is in the dative.
Bitte lassen Sie uns Ihre Bewerbungsunterlagen bis Ende der Woche zukommen.
Please send us your application documents by the end of the week.
In the meaning 'gebühren/zustehen' (to be due/to belong to someone by right), the verb requires a person in the dative. The thing that is due to this person, often something abstract like a role or honor, is the subject of the sentence.
Ihm kommt die Aufgabe zu, das Team zu leiten.
He is assigned the task of leading the team.
to be canceled / to slip one's mind / to fall to
Both verbs can describe an allocated share. With zukommen, the recipient is in the dative; with entfallen, the recipient is introduced with auf and the accusative. Thus, you say that a share kommt jemandem zu or that a share entfällt auf jemanden.

Von der Prämie kommt jedem Teammitglied der gleiche Anteil zu.
Each team member is entitled to an equal share of the bonus.
Von der Prämie entfällt auf jedes Teammitglied der gleiche Anteil.
An equal share of the bonus goes to each team member.