"提高综合素质" can be translated into English as "improve comprehensive qualities" or "enhance overall综合素质（这里'综合素质'直译为'comprehensive qualities'或更简洁的'overall qualities'，根据语境可调整） capabilities/qualities".
In more specific contexts, you might also use:
"Boost one's comprehensive abilities"（侧重于能力提升）
"Enhance one's all-around qualities"（“all-around”也表示全面的）
"Develop comprehensive personal qualities"（强调个人素质的发展）
选择哪个表达取决于具体语境和想要强调的侧重点。在大多数情况下，“improve comprehensive qualities” 或 “enhance overall qualities” 已经足够清晰和通用。