De klimmer leert inbinden en zekeren.

Klimmer is a de-word. Nouns for people are very often de nouns, and person nouns ending in -er are commonly de as well.

Compare:

• de leraar
• de bakker
• de speler
• de klimmer

So de klimmer is the correct form.

Leert is the present-tense form of leren for a third-person singular subject.

Conjugation:

• ik leer
• jij leert
• hij/zij leert
• wij leren

Because the subject is de klimmer, Dutch uses the hij/zij form, so you get leert.

Yes. That is something English speakers often notice.

Dutch leren can mean both:

• to learn
• to teach

The meaning depends on the structure.

Examples:

• Ik leer Nederlands. = I learn Dutch.
• Ik leer zwemmen. = I am learning to swim.
• Ik leer hem Nederlands. = I teach him Dutch.
• Ik leer hem zwemmen. = I teach him to swim.

In De klimmer leert inbinden en zekeren, there is no person being taught, so the natural meaning is learns / is learning.

After leren, Dutch often uses another verb in the infinitive to show what skill someone is learning.

Examples:

• leren zwemmen
• leren koken
• leren klimmen
• leren inbinden en zekeren

So in this sentence:

• leert is the conjugated verb
• inbinden and zekeren stay in their dictionary form

After leren, Dutch very often uses a bare infinitive, especially when talking about skills or activities.

So these are all natural:

• leren zwemmen
• leren koken
• leren zekeren

You can also hear leren te ... in some contexts, but leaving out te is very common and completely normal here. So De klimmer leert inbinden en zekeren sounds natural Dutch.

That is because inbinden is a separable verb.

In the infinitive, it stays together as one word:

• inbinden

But when it is the main conjugated verb in a main clause, it usually splits:

• De klimmer bindt zich in.

So in your sentence it stays together because it comes after leert and is still an infinitive.

In climbing language, Dutch often uses these verbs in a general skill sense. The context makes the missing object clear.

So:

• leren inbinden = learn how to tie in
• leren zekeren = learn how to belay

If you want to be more explicit, Dutch can do that:

• De klimmer leert zich in te binden.
• De klimmer leert een partner te zekeren.

But in general descriptions, lessons, or course outlines, the shorter version is very common.

It can mean either, depending on context.

The Dutch present tense often covers both:

• English simple present
• English present progressive

So De klimmer leert inbinden en zekeren can mean:

• The climber learns to tie in and belay
• The climber is learning to tie in and belay

If Dutch wants to stress the ongoing action more strongly, it can also say:

• De klimmer is aan het leren inbinden en zekeren.

In this sentence, they clearly belong to climbing vocabulary.

• klimmer = climber
• inbinden = tie in
• zekeren = belay / secure

Outside climbing, zekeren can also mean something like to secure more generally, but in this context the climbing meaning is the obvious one.