der Begleiter
companion
A person who accompanies someone on a journey, to an event, or through a certain period of time.
Sie besuchte den Ball in Begleitung eines eleganten Begleiters.
She attended the ball in the company of an elegant companion.

companion / accompanist
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companion
A person who accompanies someone on a journey, to an event, or through a certain period of time.
Sie besuchte den Ball in Begleitung eines eleganten Begleiters.
She attended the ball in the company of an elegant companion.

'Der Begleiter' (the companion/accompanist) is derived from the verb 'begleiten' (to accompany). The ending '-er' forms a masculine noun here that describes a person who performs this action.
Er wird mich auf meiner Reise nach Italien begleiten.
He will accompany me on my trip to Italy.
The phrase 'in Begleitung von' + dative is very common. It means that someone is somewhere or goes somewhere together with another person.
Die Kanzlerin erschien in Begleitung ihres Mannes.
The chancellor appeared in the company of her husband.
You can recognize this figurative meaning from the fact that the 'Begleiter' (companion) is not a person, but an abstract concept such as a feeling, a state, or a circumstance.
Stress ist leider ein häufiger Begleiter im modernen Arbeitsleben.
Stress is unfortunately a frequent companion in modern working life.
In a musical context, the preposition 'am' + instrument is often used to specify the role of the accompanist.
Die Sängerin trat mit ihrem Begleiter am Klavier auf.
The singer performed with her accompanist on piano.
companion / accompaniment
'die Begleitung' and 'der Begleiter' both have to do with accompanying someone or providing support. 'die Begleitung' can mean one person or several people, but also the act of accompanying. In music, 'Begleitung' also means the backing music or accompaniment. 'der Begleiter', on the other hand, is a single male person who accompanies someone, or a musician who provides support. Learners may confuse the words because both belong to 'begleiten' (to accompany). As a practical rule: if you mean the person, 'der Begleiter' fits. If you mean the situation, the help, or a group, 'die Begleitung' is often better.

Der Begleiter wartete vor dem Kino, bis Anna aus dem Bus stieg.
The companion waited in front of the cinema until Anna got off the bus.
Für den Arzttermin braucht mein Großvater eine Begleitung.
My grandfather needs someone to accompany him to the doctor's appointment.