aufkommen
to arise
To arise, develop, or rise up. Often used for feelings, thoughts, moods, or trends.
Langsam kam Panik in der Menge auf.
Panic slowly arose in the crowd.

to arise / to cover
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to arise
To arise, develop, or rise up. Often used for feelings, thoughts, moods, or trends.
Langsam kam Panik in der Menge auf.
Panic slowly arose in the crowd.

'Aufkommen' (to arise/to cover) is a separable verb. In a main clause, the prefix 'auf' goes at the end. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Ein starker Wind kam am Abend auf.
A strong wind picked up in the evening.
The prefix 'auf-' in combination with 'kommen' (to come) often conveys the idea of a beginning or upward movement. Something begins to exist or appears, like rising smoke.
Plötzlich kam eine seltsame Stimmung auf.
Suddenly, a strange mood arose.
In the meaning 'entstehen' (to arise), the subjects are usually abstract nouns. Typical combinations are: 'Zweifel kommen auf' (doubts arise), 'ein Verdacht kommt auf' (a suspicion arises), 'Freude kommt auf' (joy arises), or 'eine Frage kommt auf' (a question arises).
Bei seiner Erzählung kamen mir erste Zweifel auf.
As he told his story, my first doubts arose.
When 'aufkommen' is used in connection with the weather, it describes the approach or beginning of a weather phenomenon. Typical subjects are 'Wind' (wind), 'Sturm' (storm), 'Nebel' (fog), or 'Gewitter' (thunderstorm).
Laut Wetterbericht soll morgen ein Sturm aufkommen.
According to the weather forecast, a storm is supposed to pick up tomorrow.
In the meaning 'bezahlen' (to pay), 'aufkommen' is always used with the preposition 'für' and the accusative. The structure is: 'jemand kommt für etwas auf' (someone covers something).
Wer kommt für den entstandenen Schaden auf?
Who will cover the damage that occurred?
to pay
'bezahlen' and 'aufkommen für' can both mean that someone gives money for something. 'bezahlen' is the normal word for a bill, goods, or a service. 'aufkommen für' is used more when someone covers the costs or is financially responsible for damage. It sounds somewhat more formal and usually needs 'für'. The words are easy to confuse because both are about money. In everyday life, people often say 'bezahlen'; when responsibility for costs is involved, 'aufkommen für' is more precise.

Die Versicherung kommt für den Schaden am Auto auf.
The insurance company covers the damage to the car.
Der Mitarbeiter bezahlt im Gartenmarkt die neuen Pflanzen.
The employee pays for the new plants at the garden center.