einlaufen
to enter
Refers to ships or boats entering a harbor or bay.
Das große Kreuzfahrtschiff wird morgen früh in den Hafen einlaufen.
The large cruise ship will enter the harbor early tomorrow morning.

to enter / arrive / shrink
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to enter
Refers to ships or boats entering a harbor or bay.
Das große Kreuzfahrtschiff wird morgen früh in den Hafen einlaufen.
The large cruise ship will enter the harbor early tomorrow morning.

'Einlaufen' (to enter / arrive / shrink) is a separable verb. The prefix 'ein-' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Die Flotte läuft in den sicheren Hafen ein.
The fleet enters the safe harbor.
Since 'einlaufen' (to enter / arrive / shrink) describes movement or a change of state in all of its meanings, the perfect tense is always formed with the auxiliary verb 'sein' (to be).
Die E-Mail mit der Bestätigung ist soeben eingelaufen.
The email with the confirmation has just arrived.
The prefix 'ein-' often suggests movement 'hinein' (into/inward). This applies literally to ships (into the harbor), athletes (into the stadium), and runners (into the finish), but also figuratively to clothing that gets smaller (shrinks inward).
Die Mannschaft ist pünktlich zum Anpfiff eingelaufen.
The team entered right on time for kickoff.
When the subject of the sentence is something abstract, 'einlaufen' usually means 'ankommen' (to arrive) or 'eingehen' (to come in / be received). Typical subjects are messages, orders, payments, applications, or complaints.
Bis zum Fristende sind über hundert Bewerbungen eingelaufen.
By the deadline, more than one hundred applications had arrived.
When clothing shrinks, the person this happens to can be in the dative. This is a very typical construction in German.
Die neue Jeans ist mir leider beim ersten Waschen eingelaufen.
Unfortunately, the new jeans shrank on me the first time I washed them.
In the meaning 'to make shoes more comfortable', 'einlaufen' is used as a transitive verb with an accusative object. The fixed expression is '(die) Schuhe einlaufen' (to break in shoes).
Ich trage die neuen Schuhe zu Hause, um sie für die Party einzulaufen.
I wear the new shoes at home to break them in for the party.
to arrive
'ankommen' and 'einlaufen' can both mean that something or someone reaches a destination. 'ankommen' is the general word and works for people, trains, packages, and many other situations. 'einlaufen' is more specific: it is especially used for ships entering a harbor, for messages or payments that arrive, or for runners reaching the finish. Learners may confuse the words because both describe an arrival. In most everyday situations, 'ankommen' is correct; 'einlaufen' is chosen only in certain fixed areas.

Am Nachmittag ist die Zahlung endlich auf dem Konto eingelaufen.
In the afternoon, the payment finally arrived in the account.
Wegen einer Störung kommt der Zug erst um acht Uhr an.
Because of a disruption, the train will not arrive until eight o'clock.