When someone arrives at a place, you can talk about their arrival there. This is rather formal use.

His arrival was hardly noticed.

A week after her arrival, we had a General School Meeting.

If you want to say that something happens immediately after someone arrives at a place, you can use a phrase beginning with on. Note that you must use on, not 'at', in sentences, like these. You do not say, for example, 'At his arrival in London, he went straight to Oxford Street. You can say 'On his arrival in London, he went straight to Oxford Street'.

On his arrival in Singapore he hired a secretary and rented his first office.

The British Council will book temporary hotel accommodation on your arrival in London.

The possessive determiner is often omitted. For example, instead of saying 'on their arrival', you can just say on arrival.

The principal guests were greeted on arrival by the Lord Mayor of London.

On arrival at the Station hotel in Dumfries he acknowledges a few familiar faces.