AFAIK clearly the Aruba 3810M can be kept synchronized - and this is true at least since the release of first KB.16.01 - with external Time Sources (so the Switch, from this point of view, is acting essentially as a client that pull time reference from one or more time reference servers) using various time synchronization methods (TIMEP, SNTP or NTP).
The Switch also has an internal system clock (I don't believe that internal system clock is "battery backed" to retain - after a power outage or a power off/on cycle - the time, date and timezone/DST settings) that can be manually set [*] through some CLI commands (e.g. clock/time).
I don't believe that, actually, the Aruba 3810M can act as a NTP Server...so being a Time Source for NTP Clients (as reference read the Chapter 2 "Time synchronization" of HPE ArubaOS-Switch Management and Configuration Guide for K/KA/KB.16.02, November 2016 edition).
[*] example: the time [<hh>:<mm>[:<ss>]][<mm>/<dd>/[<yy>]<yy>] command.