This study quantifies the shock transmission mechanism between the trade policy uncertainty (TPU) index and Sharia-compliant stock sectoral conditional volatility in the Gulf Cooperation Council (GCC) countries. We employ a comprehensive analysis that includes the time-domain extended joint and frequency-domain quantum vector autoregressive (QVAR) frameworks. The time-domain QVAR demonstrates that TPU causes the most substantial shocks to utility sector volatility. Investors in the GCC must strategically allocate their investment portfolios to the consumer services and energy industries, which are less vulnerable to the TPU shock. The results show that TPU shocks provide more error variances to the long-term and bullish conditional volatility (or higher quantiles) of the utility, real estate investment trust funds (REIT), healthcare, and industry sectors. Conversely, during bearish volatility conditions (lower quantiles), TPU shocks result in higher shocks in the conditional volatility of the utility, REIT, finance, and industrial sectors. Long-term investors should diversify their portfolios to mitigate risk in the utility, REIT, and industry sectors through strategic investments in consumer service sector. However, in the short term and during both bearish and bullish sectoral volatility, the consumer service and industry sectors are more vulnerable to TPU shocks. Regarding diversity, the REIT, energy, and financial sectors are the least affected by TPU shocks, offering a protective buffer in the short term and during periods of higher and lower GCC Islamic sectoral volatility.