What is standard applied? ISO 10628, ISO 14084, ISO 14617, ISO 15519, PIC001, ANSI/ISA-5.1 or custom?

There is a bit of a variety and I suppose it depends a bit on what actual type of pump it is.

I would be tempted to just draw a square box with MP in the middle and a motor attached so that you can turn it on and off or control the speed and then define it in the legend sheet.

Those ISO symbols look Horrible IMHO.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

Good question shvet! The P&ID's have been developed by the client (who is UK based) over a number of years without real specific reference to one of the available standards, other than (probably) BS 1646-1 which is now withdrawn.
But in answer to your question, it would probably be against BS EN ISO 10628. (Although I don't have a copy of that one so I don't know whether 'metering pumps' are categorised in that).

I'm tempted to follow the approach of LittleInch and just 'black box' it. This would be better than the misleading centrifugal pump symbol currently in use.

I have seen row 8, position 2 used, but row 7, position 1 looks good.

As you are probably aware, there is no universal standard for preparing a P&ID. Most experienced engineers would probably recognize the application particularly by the pumping characteristics (if you have that on the P&ID) no matter what symbol you use.

A metering pump is usually one of the many types of pd pumps, for each of which there is a typical P&I D symbol - use the appropriate one. It matters not what function the pump is in, as far as the symbol used is concerned.

Equipment is shown in P&ID more at design than function. P&ID intends to reflect resulted process design rather than process designer's intentions. Otherwise a user is prone to human errors being confused by designer's mentality.

ISO 10628-2-2012