Query takes long time to execute while there is an index configured
Perhaps auto-update stats kicked in. AUTO_UPDATE_STATISTICS_ASYNC ON is your friend in that case. Check the index stats date to see if it coincides with the slowness:
SELECT 
    STATS_DATE(
          OBJECT_ID(N'YourSchema.YourTable')
        , INDEXPROPERTY(OBJECT_ID(N'YourSchema.YourTable'),N'YourIndexName','IndexID')
    ) AS LastStatsDate;

-- dan-guzman
If it isn't plan generation (SET STATISTICS TIME ON can be revealing), or the query processing per se (reading just a few rows with a pretty unique index), then the natural thing to suspect is blocking. - tibor-karaszi

There are several ways to monitor for statistics update events (profiler, extended events...). SQL Server 2019 introduces the WAIT_ON_SYNC_STATISTICS_REFRESH wait type, which can appear in the wait information section of 'actual' execution plans.
Sentry One Plan Explorer captures statistics building and refreshing (statman) and includes this information in the wait info.