Secondary Return Pump

[AMW93]

Hi guys, looking for a bit of help.
Recently qualified plumber but having an issue as my manager is away on holiday!
Getting hot water at taps but it's taking quite a while to come through at certain outlets, I'm thinking it will be a faulty pump but I'm not all that sure on how to fully check that it is before I go and buy a new one for the client.
It's an unvented system, newly piped in but old pump used.
Any help greatly appreciated. Cheers

 

[picasso]

How is the return connection made to the cylinder ?

 

[oldbuffer]

I'd first check supply to secondary pump to make sure its switched on. Also, many of these have timers attached, so its worth checking the timer is set to the correct time and is calling for circulation at the required times.