Learn Hardcore Portuguese (Portugal): Procuro uma veterinária que trate a minha gata com carinho. - I’m looking for a female vet who treats my cat gently.

Because the clause describes an as‑yet unknown or desired person. In Portuguese, a relative clause after an indefinite/unknown antecedent typically takes the present subjunctive: uma veterinária que trate…. Contrast:

Known/specific: Já tenho a veterinária que trata a minha gata com carinho. (indicative)
Desired/unknown: Procuro uma veterinária que trate a minha gata com carinho. (subjunctive)

Does Procuro mean “I’m looking for”? Do I need a progressive form?

Yes. Simple present Procuro naturally covers “I’m looking for” in Portuguese. You can also say:

Estou à procura de uma veterinária… (very common in Portugal)
Estou a procurar uma veterinária… (also fine in European Portuguese) Avoid Brazilian-style Estou procurando in Portugal.

Is procurar por acceptable in European Portuguese?

In Portugal, the standard is to use procurar without a preposition: Procuro uma veterinária…. The form procurar por is common in Brazil but is generally avoided in European Portuguese in this sense.

Why the feminine uma veterinária? What if the vet’s gender doesn’t matter?

Veterinária is the feminine form (a female vet); veterinário is masculine. If gender is unknown or irrelevant, Portuguese typically defaults to the masculine: um veterinário. In careful or inclusive writing you’ll sometimes see um(a) veterinário(a), but in speech people usually pick one.

Why is it a minha gata instead of just minha gata?

European Portuguese normally uses the definite article before possessives: a minha gata, o meu carro, a nossa casa. In Brazil, dropping the article (e.g., minha gata) is more common. In Portugal, omitting the article can sound non-native in most contexts.

What’s the difference between tratar a minha gata and tratar da minha gata?

tratar alguém (bem/mal/com carinho) = to treat someone (in some manner). Here: tratar a minha gata com carinho = “treat my cat with affection.”
tratar de alguém = to look after/take care of someone; also “to deal with.” tratar da minha gata suggests ongoing care/looking after, not the manner of treatment. Both are correct but carry different nuances.

Can I replace a minha gata with a pronoun? Where does it go?

Yes: Procuro uma veterinária que a trate com carinho. After que, European Portuguese strongly prefers proclisis (pronoun before the verb): que a trate. Enclisis (trate-a) is not used after que in EP.

Why que and not quem?

Here que is a relative pronoun referring back to uma veterinária. You could also say Procuro quem trate a minha gata com carinho, where quem stands for “whoever” without a stated antecedent. Both are correct; your original sentence specifies the noun first, so que is the natural choice.

Can I move com carinho earlier in the clause?

Yes, but the most natural spots are:

…que trate a minha gata com carinho. (most common)
…que a trate com carinho. You can say …que trate com carinho a minha gata, which is acceptable but a bit less common in everyday speech. Placing com carinho right after que is unusual.

Does gata just mean a female cat? Any slang I should know?

Yes, gata is the female of gato. For a male cat, say o meu gato. Colloquially, gata can mean an attractive woman (and gato, an attractive man), but in this veterinary context there’s no ambiguity.

How do I pronounce the sentence in European Portuguese?

Approximate EP pronunciation:

IPA: [pɾuˈkuɾu umɐ vɨtɨɾiˈnaɾjɐ kɨ ˈtɾatɨ ɐ ˈmiɲɐ ˈɡatɐ kõ kɐˈɾiɲu]
Rough guide: pro-KOO-roo oo-mɐ vuh-te-ree-NAH-ryɐ kih TRAH-tih ɐ MEE-nyɐ GAH-tɐ kong kah-REE-nyoo

Could I say com cuidado or bem instead of com carinho?

com carinho = with affection/warmth/gentleness (emotional nuance).
com cuidado = carefully, with caution/attention (technical or safety nuance).
bem = well; que trate bem a minha gata focuses on good treatment in general. Choose based on the nuance you want.

Is Procuro too direct? How can I make it more polite?

It’s already polite and neutral. Softer options:

Estou à procura de uma veterinária que…
Queria/Precisava de uma veterinária que… (conditional/past-imperfect to soften)
Inquiries: Ando à procura de… (I’ve been looking for…)

Why is the verb form trate and not tratar or trates?

In the relative clause, the subject is que referring to uma veterinária (third person singular). Present subjunctive of tratar in 3rd person singular is trate:

eu trate, tu trates, ele/ela/você trate, nós tratemos, vocês/eles/elas tratem. So it must be que [ela] trate.