"给予自治权" can be translated into English as "grant autonomy" or "confer autonomy".
"Grant autonomy" emphasizes the act of officially giving or allowing someone or something the right to govern themselves or make their own decisions.
"Confer autonomy" has a similar meaning, with "confer" implying the bestowal or granting of a right or privilege.
Both expressions are commonly used in contexts where discussions about governance, decentralization, or the empowerment of regions or groups arise.