aiohttp check headers on every request and set them again if not correct

We are deciding whether to integrate aiohttp to our app (FastAPI) but I am having trouble understanding the logic needed to send authenticated requests using headers that have expiration time.

The provider we want to connect to requires us to first authenticate by sending a POST request to an endpoint that returns a key and a signature to use as a header for subsequent requests. The problem is that these values have a very short expiration time and I need to check all requests to see if they are still valid.

We define a class that we use to raise/stop the aiohttp client session and reuse it throughout the application:

import aiohttp


class HttpClient:
    session: aiohttp.ClientSession = None

    def start(self):
        self.session = aiohttp.ClientSession()

    async def stop(self):
        await self.session.close()
        self.session = None

    def __call__(self) -> aiohttp.ClientSession:
        assert self.session is not None
        return self.session


http_client = HttpClient()

Then we make the requests by importing this session:

import aiohttp

from app.core.http_client import http_client
from fastapi import APIRouter, Depends

router = APIRouter()

@router.get("/some-endpoint")
async def some_endpoint(http_client: aiohttp.ClientSession = Depends(http_client)):
    url = "http://example.com/"
    headers = { ... }
    async with http_client.get(url, headers=headers) as response:
        return await response.json()

How can I check if the headers are correct each time and, in case they have expired, get them again and resend the requests?

Is there a way to create a middleware for the client session that runs on every requests? Thanks in advance!