der Aufstieg
ascent
The movement upward, for example when climbing a mountain or going up stairs.
Der Aufstieg auf den Gipfel dauerte vier Stunden.
The ascent to the summit took four hours.

ascent / rise
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ascent
The movement upward, for example when climbing a mountain or going up stairs.
Der Aufstieg auf den Gipfel dauerte vier Stunden.
The ascent to the summit took four hours.

'Aufstieg' (ascent / rise) is derived from the separable verb 'aufsteigen' (to ascend / rise) (auf + steigen). It literally describes the process of 'Nach-oben-Steigens' (climbing upward). This basic idea appears in all meanings, whether on a mountain or in a career.
Nach seinem Aufstieg in der Firma hatte er mehr Verantwortung.
After his rise in the company, he had more responsibility.
The adjective 'steil' (steep) is often combined with 'Aufstieg' (ascent / rise), even in figurative meanings. A 'steiler Aufstieg' (steep rise) describes a very fast and impressive development, whether on a mountain or in a career.
Die Band erlebte nach ihrem ersten Hit einen steilen Aufstieg.
The band experienced a steep rise after their first hit.
In the literal meaning, 'Aufstieg' (ascent) is often combined with prepositions that describe the destination. Common are 'der Aufstieg auf (+ Akk.)' (the ascent to/up a summit) for a peak or 'der Aufstieg zu (+ Dat.)' (the ascent to) for a place.
Der Aufstieg auf die Zugspitze ist sehr anspruchsvoll.
The ascent of the Zugspitze is very demanding.
In the context of careers and society, people often speak of 'beruflicher Aufstieg' (career advancement) or 'sozialer Aufstieg' (social mobility / social rise). The target position is indicated with 'zum/zur'.
Ihr beruflicher Aufstieg zur Managerin war beeindruckend.
Her career rise to manager was impressive.
In a sports context, the fixed expression 'der Aufstieg in (+ Akk.)' (promotion to/into) is key. It describes the move to a higher league.
Der Verein feierte den Aufstieg in die zweite Liga.
The club celebrated promotion to the second division.
The phrase 'Aufstieg und Fall' (rise and fall) is a very well-known fixed expression. It is often used to summarize the history of empires, companies, or influential people.
Das Buch beschreibt den Aufstieg und Fall des berühmten Schauspielers.
The book describes the rise and fall of the famous actor.
career
'Karriere' and 'Aufstieg' can both describe someone advancing professionally. 'Karriere' means a person's whole professional path, over a longer period of time. 'Aufstieg' is more about the upward step or the improvement in position, for example from employee to team leader. So an 'Aufstieg' can be part of a 'Karriere'. The words can be confused because both have to do with professional success. If you are talking about the whole development, 'Karriere' fits better; if you mean the step into a higher position, 'Aufstieg' is more precise.

Der Aufstieg zur Abteilungsleiterin war für Anna ein großer Erfolg.
Anna's rise to department head was a great success.
Ihre Karriere begann in einer kleinen Firma und führte sie später ins Ausland.
Her career began in a small company and later took her abroad.