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.

'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 expect
'erwarten' and 'auf jemanden zukommen' can both talk about something in the future. 'erwarten' means that you expect something or believe that it will happen. So the focus is on your own assessment. 'auf jemanden zukommen' more often means that a task, event, or problem lies ahead in the future. The focus is on what will happen soon and affect someone. Learners may confuse the words because both point to the future. As a guide: you 'erwartet' a result, a message, or an event; an exam, a conversation, or a lot of work 'kommt auf jemanden zu'.

In den nächsten Wochen kommt viel Arbeit auf das Team zu.
In the next few weeks, a lot of work will be coming the team's way.
Maria erwartet heute eine Antwort auf ihre Bewerbung.
Maria expects an answer to her application today.