Learn French: Je suis content que tu aies reçu l'approbation du directeur. - I am glad that you received the director's approval.

The phrase Je suis content que expresses an emotion, which forces the following verb into the subjunctive mood. Because the action of receiving happened before the feeling of being glad, we use the past subjunctive. It is built just like the passé composé, but the auxiliary verb (avoir) is conjugated in the subjunctive (aies).

How does the meaning change if I say que tu reçoives (present subjunctive) instead?

Using the present subjunctive tu reçoives means the action is happening right now or in the future: I am glad that you are receiving it. The past subjunctive aies reçu specifically shows anteriority, meaning the approval was already completely received before the moment you felt glad.

Could I avoid the subjunctive here by using an infinitive, like d'avoir reçu?

Not in this sentence, because there are two different subjects (je and tu). You can only use the infinitive construction (for example, Je suis content d'avoir reçu) when the person experiencing the emotion is the exact same person performing the action.

Since approbation ends in -tion, is it always feminine?

Yes! As a helpful rule of thumb, almost all French nouns ending in -tion are feminine. Even though we use l' here because it starts with a vowel, any adjectives describing it would need to agree in the feminine form.