the doctor suggested that he ——an operation at once.

have
suggest做建议讲时 后面接that引导的宾语从句要用虚拟语气Should加上动词原形,should可以省略
完整的是：
the doctor suggested that he should have an operation at once.
与suggest相同的还有insist order demand 等,表命令 建议 要求 坚持