BleakClient suggests "async with", but how can I get a handle that lasts beyond my code block?

I wrote a Python script using the bleak Bluetooth Low Energy client that works from a command line. I want to split the script into REST endpoints.

To that end, I want to replace async with BleakClient(d, timeout=10) as client: with something that allows me to make client global so that I can use it in another REST endpoint. In other words, I want client to hang around beyond the call that connects to the device. Any ideas?

I tried client = await BleakClient(d, timeout=10) but this line throws an exception: object BleakClient can't be used in 'await' expression.

EDIT

I am including the entire (truncated) Python script. Call to ConnectAndReadChar() works. Call to ConnectUUT() does not work. Exception on line 'client = await BleakClient(d, timeout=10)', <class 'TypeError'>.

import asyncio
import traceback
from bleak import BleakScanner, BleakClient
import sys
import time

global client
        
async def ConnectAndReadChar(MAC_ID):
    d = await BleakScanner.find_device_by_address(MAC_ID, timeout=20)            
    time.sleep(0.5)
    while True:
        try:
            if d.address == MAC_ID:
                async with BleakClient(d, timeout=10) as client:
                    time.sleep(0.5)
                    res = await client.pair(protection_level=None)
                    print(res)

                    x = client.is_connected
                    print("Connected: {0}".format(x))

                    svc = client.services.get_service("Service ID")

                    thisCharacteristic = svc.get_characteristic("Char ID")
                    value = bytes(await client.read_gatt_char(thisCharacteristic))
                    print("\tValue: {0} ".format(value))

                    await client.disconnect()
                    await client.unpair()
            return
        except:
            e = sys.exc_info()[0]
            print(e)


async def ConnectUUT(MAC_ID):
    global client
    d = await BleakScanner.find_device_by_address(MAC_ID, timeout=20)            
    while True:
        try:
            if d.address == MAC_ID:
                # async with BleakClient(d, timeout=10) as client:
                client = await BleakClient(d, timeout=10)
                if client is not None:
                    time.sleep(0.5)
                    res = await client.pair(protection_level=None)
                    print(res)

                    x = client.is_connected
                    print("Connected: {0}".format(x))
            return
        except:
            e = sys.exc_info()[0]
            print(e)

async def ReadFrames():
    global client

    try:
        svc = client.services.get_service("Service ID")
        thisCharacteristic = svc.get_characteristic("Char ID")
        return
    except:
        e = sys.exc_info()[0]
        print(e)

async def DisconnectUUT():
    global client

    try:
        await client.disconnect()
        await client.unpair()
    except:
        e = sys.exc_info()[0]
        print(e)
    return

async def main():
    await ConnectAndReadChar("MAC ID goes here")

    await ConnectUUT("MAC ID goes here")
    await ReadFrames()
    await DisconnectUUT()
        
if __name__ == "__main__":
    asyncio.run(main())

If you use a BleakClient as an async context manager, it implicitly performs a connect. You can also do this explicitly:

client = BleakClient(d, timeout=10)
await client.connect()