Why in this sentense Can the cat climb the tree?, you will not add s to climb

It's the presence of "can" that changes the verb to a perfect tense.

The cat climbs the tree.
The cat can climb the tree.
Can a cat climb a tree?

You're right that it is the presence of 'can' that determines no 's', E, but there is no "perfect tense".

[And actually, the perfect isn't a tense, it's an aspect.

When a lexical verb - climb, run, jump, look, etc is used with a modal verb - can, could, may, might, will, would, should, shall, etc third person - he, she, it never attracts an 's'.