streben nach
to strive for
To make a great effort, with ambition, to achieve a goal or ideal.
Viele Menschen streben nach Glück und Anerkennung.
Many people strive for happiness and recognition.

to strive
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to strive for
To make a great effort, with ambition, to achieve a goal or ideal.
Viele Menschen streben nach Glück und Anerkennung.
Many people strive for happiness and recognition.

The verb 'streben' (to strive) is somewhat elevated and is often used in written language or formal contexts. It sounds more ambitious and goal-oriented than everyday verbs.
Der junge Künstler strebt nach Perfektion in seinen Werken.
The young artist strives for perfection in his works.
When referring to achieving a goal, 'streben' is always used with the preposition 'nach' and the dative. You strive for something.
Er hat sein ganzes Leben lang nach Reichtum gestrebt.
He strove for wealth his whole life.
In the meaning 'sich bemühen' (to make an effort), 'streben nach' is often combined with abstract goals. Typical examples are: 'nach Erfolg streben' (to strive for success), 'nach Macht streben' (to strive for power), or 'nach Freiheit streben' (to strive for freedom).
Die politische Bewegung strebt nach sozialer Gerechtigkeit.
The political movement strives for social justice.
You can recognize the architectural or physical meaning by the fact that the verb is usually used without the preposition 'nach'. It describes movement or orientation in a direction.
Die Äste des Baumes streben alle zum Licht.
The branches of the tree all reach toward the light.
to follow / pursue
'verfolgen' and 'streben nach' can both mean that someone wants to achieve a goal. 'verfolgen' fits well when it is about a concrete plan or a clear intention that you carry forward step by step. 'streben nach' sounds more like ambition, an ideal, or a strong desire, for example for success, freedom, or recognition. Learners may confuse the words because both express a goal. In practical terms: you 'verfolgen' a plan, and you 'streben nach' an ideal.

Viele Menschen streben nach einem sicheren Leben und guter Arbeit.
Many people strive for a secure life and good work.
Im neuen Projekt verfolgen wir das Ziel, weniger Energie zu verbrauchen.
In the new project, we are pursuing the goal of using less energy.