India and Pakistan are so often at odds that there is a tendency to shrug off their spats, but not since their most recent, full-blown war in 1971 has the risk of escalation been so high.

黑体部分等于：

but since their most recent, full-blown war in 1971, the risk of escalation has not been so high.

即主句的not移至since从句之前，导致主句部分倒装。这种结构类似于not until引导的从句导致主句部分倒装一样。