The area of the screen where the expanded toolbar appears occludes a
significant part of the screen.
In the sentence above we see the two present tense verbs appears and occludes next to each other. The verb occludes means something similar to hides.
We might think that these verbs are chained together like the verbs can and swim in the sentence:
Or maybe they might look as if they are chained together like wants and to leave in:
However, in the Original Poster's sentence, the verb appears is part of the noun phrase:
- The area of the screen where the expanded toolbar appears
This noun phrase is functioning as the Subject of the sentence. The noun phrase includes a relative clause:
- where the expanded toolbar appears
The verb appears occurs within this relative clause.
In contrast, the verb occludes is the main verb in the main clause.
The two verbs have different Subjects. The Subject of occludes is "The area of the screen where the expanded toolbar appears". The Subject of appears is "the extended toolbar".
We can structure the larger sentence like this:
- [The area of the screen where the expanded toolbar appears] occludes a
significant part of the screen.
In answer to the Original Poster's question: yes, this sentence is perfectly grammatical.
Nonetheless, the Original Poster's intuitions are also correct. We cannot chain two tensed verbs together in English. We can only have one tensed verb in a verb phrase. In their example though, these verbs are in different verb phrases.