Firmamos a condición de que revisemos el historial veterinario.

It can be either one in isolation, because for -ar verbs the nosotros form of the present and the preterite is spelled the same:

• firmamos = we sign / we are signing
• firmamos = we signed

Here, the context makes it clear that it means the present with a future sense: we sign / we’ll sign.

The clue is the rest of the sentence: a condición de que revisemos... refers to a condition that still needs to be met, so this is not talking about a completed past action.

Spanish often uses the present tense to talk about a future action, especially when the action is seen as planned, agreed, or immediate.

So both of these can work:

• Firmamos a condición de que...
• Firmaremos a condición de que...

The version with firmamos can sound a bit more direct or immediate, like we’ll sign, provided that...

Because Spanish usually omits subject pronouns when the verb ending already shows who the subject is.

• firmamos already means we sign / we signed
• revisemos already means that we review

So nosotros is unnecessary unless you want to add emphasis or contrast:

• Nosotros firmamos, pero ellos no.

In the original sentence, leaving out nosotros is the most natural choice.

It introduces a condition. It means something like:

• on condition that
• provided that

It is a fairly formal expression. It connects the main action (firmamos) to the requirement that must be satisfied (que revisemos el historial veterinario).

So the structure is:

• main action
  • a condición de que
    • subjunctive clause

Because a condición de que is a fixed expression.

The noun condición is linked with de, and then que introduces the following clause:

• a condición de que revisemos...

So this is not an optional extra de. It belongs to the phrase.

You should learn a condición de que as one chunk.

Because a condición de que triggers the subjunctive.

In Spanish, when you talk about a condition, requirement, or something that is not yet a confirmed fact, the verb in the subordinate clause often goes in the subjunctive.

Here, reviewing the veterinary record is not presented as a fact. It is something that must happen first, as a condition for signing. That is why Spanish uses:

• revisemos
  not
• revisamos

It comes from the verb revisar.

For the present subjunctive, you start from the yo form of the present indicative:

• yo reviso

Then remove the -o and add the subjunctive endings. For -ar verbs, the nosotros ending is -emos:

• revis-
  • emos = revisemos

So:

• revisar → yo reviso → revisemos

Normally, no. After a condición de que, standard Spanish uses the subjunctive, so revisemos is the correct form.

• a condición de que revisemos... ✔
• a condición de que revisamos... ✘

Using revisamos would sound ungrammatical to most native speakers in this structure.

Because historial and historia are not exactly the same.

• historial usually means a record, file, or history of previous events, especially in administrative or medical contexts.
• historia often means story or history in a broader sense.

So el historial veterinario means the animal’s veterinary record / medical history. That is the natural phrase here.

Because in Spanish, descriptive and classifying adjectives usually come after the noun.

So:

• historial veterinario = veterinary record

Here, veterinario tells you what kind of record it is. This kind of adjective normally follows the noun in Spanish.

Yes, sometimes Spanish can rephrase this kind of idea, but the original structure is perfectly valid.

Because the subject is we in both parts, a learner may expect an infinitive, but Spanish often keeps the full clause after expressions like a condición de que:

• Firmamos a condición de que revisemos el historial veterinario.

A possible rewording might be more like:

• Firmamos con la condición de revisar el historial veterinario.

But that is a different phrasing, not a direct replacement in every context. The original sentence is a standard and correct way to express the idea.

It is correct and natural, but it sounds a bit formal or careful. In everyday speech, people might sometimes prefer simpler alternatives depending on the context, such as:

• si
• siempre que
• con tal de que

But a condición de que is very useful to know because it is common in formal speech, contracts, negotiations, and precise statements.