Monitor SQL Server stored procedure latency
Stored procedure execution statistics are surfaced via the sys.dm_exec_procedure_stats dynamic management view.

This query will show stats for stored procedures in the current database:

SELECT ObjectName = s.name + N'.' + o.name
    , sps.last_execution_time
    , sps.execution_count
    , sps.last_elapsed_time
    , sps.total_elapsed_time
    , avg_elapsed_time = sps.total_elapsed_time / sps.execution_count
FROM sys.dm_exec_procedure_stats sps
    INNER JOIN sys.objects o ON sps.object_id = o.object_id
    INNER JOIN sys.schemas s ON o.schema_id = s.schema_id
WHERE sps.database_id = DB_ID()
ORDER BY s.name
    , o.name;


The output looks like:

╔══════════════════════════════════╦═════════════════════════╦═════════════════╦═══════════════════╦════════════════════╦══════════════════╗
║            ObjectName            ║   last_execution_time   ║ execution_count ║ last_elapsed_time ║ total_elapsed_time ║ avg_elapsed_time ║
╠══════════════════════════════════╬═════════════════════════╬═════════════════╬═══════════════════╬════════════════════╬══════════════════╣
║ dbo.procAccessUniqueID           ║ 2018-09-07 13:21:04.403 ║          173346 ║               614 ║          223886470 ║             1291 ║
║ dbo.procAddBatchClassFilter      ║ 2018-09-04 15:25:22.150 ║              43 ║              5124 ║             171329 ║             3984 ║
║ dbo.procAddBatchFilter           ║ 2018-09-06 15:04:34.817 ║              17 ║               251 ║              18767 ║             1103 ║
║ dbo.procAddLock2                 ║ 2018-09-07 13:21:05.047 ║          373086 ║               912 ║          542911271 ║             1455 ║
║ dbo.procAddTempUser_V10          ║ 2018-09-07 10:50:13.973 ║               4 ║               292 ║               1223 ║              305 ║
║ dbo.procAddUserGroupRelationship ║ 2018-09-07 13:14:49.533 ║            1124 ║                70 ║             151824 ║              135 ║
╚══════════════════════════════════╩═════════════════════════╩═════════════════╩═══════════════════╩════════════════════╩══════════════════╝ 

The avg_elapsed_time, measured in microseconds, shows the average elapsed time for completed executions of each stored procedure listed.