MCP Client connecting to an already running MCP Server?

[sidharthrajaram]

In the example, the MCP Client is responsible for starting the MCP server process like:

from mcp import ClientSession, StdioServerParameters
from mcp.client.stdio import stdio_client

# Create server parameters for stdio connection
server_params = StdioServerParameters(
    command="python", # Executable
    args=["example_server.py"], # Optional command line arguments
    env=None # Optional environment variables
)

async def run():
    async with stdio_client(server_params) as (read, write):
        async with ClientSession(read, write) as session:
            # Initialize the connection
            await session.initialize()
            ...

Let's say I have the MCP server running already (i.e. uv run example_server.py).

How can MCP clients connect to that server?

Thank you!