So, you have to pass both the historical and live data.

Aggregate the data first and then pass in Supertrend function you will get the accurate value.
Eg code below:

def get_supertrend_input(symbol, live_candles):
    # Fetch historical 
    query = "GET HISTORICAL DATA"
    values = [symbol, "minute"]
    historical_candles = fetch_historical_data(query, values)
    # Merge
    all_candles = historical_candles + live_candles
    # Safety check
    if len(all_candles) < 15:  # minimum for ATR(10)
        return []
    return all_candles

def run_supertrend(symbol, live_candles):
    candles = get_supertrend_input(symbol, live_candles)
    if not candles:
        return None
    result = compute_supertrend(candles, period=10, multiplier=3)
    if not result:
        return None
    return result[-1]  # latest signal