The shoot coming up from the earth is from the root stock - whatever the standard was grafted to. That shoot should be cut out immediately or it will suck the life out of your standard and the whole top will die. You'll be left with whatever that root stock is. I'm sure you know that oleander is among the most poisonous of shrubs - just brushing against it can cause a rash. Wear long sleaves & heavy gardening gloves when dealing with this shrub. I don't know a lot about oleander. They are more common in the South, US & temperate areas, but I do know they are poisonous.

Oh you caught me there it is 100% below soil level. Never seen on oleander before. I think mine is from Spain or Italy a few yrs old but now leggy. Cream coloured

Here's a ghost story with oleander at the center. Not sure if it's true or folklore, but explains why oleander has so much "baggage". attached. Could be just folklore, but makes a scary ghost story, lol!
http://themoonlitroad.com/slave-girl-myrtles-plantation-louisiana-ghost-story/

Now is not the time to cut oleander in the UK anyway - but you say yours is a standard form; as far as I'm aware, these plants are not grafted onto different rootstocks, so if you've got a shoot coming up from below soil level, it might well be the oleander.This can happen over time, particularly if the top parts aren't doing fine, but you can tell by examining the plant. Check the top of the long, straight stem, right at the top where the branches start growing from and are clustered - if its grafted, you should be able to see the graft there, it'll look like a knobbly, lumpy bit.

Did you intend it to be a standard or bush? makes a difference to what you chop.

IF the shoot is coming from below the graft, it's not the plant you thought you were getting. It should be dealt with immediately, before it gets larger.

Oleanders are rarely grafted, Bathgate, but normally grown from cuttings. Granted, a few standards are a dwarf cultivar of oleander grafted on top of a long cutting of a full size variety. If that is the case, the graft will be very obvious at the base of the crown of the "tree",and, as Bathgate says, anything growing from below the graft should be removed.

Ah. It looks like a standard now but is not. So I have good growth high up 20 inches up with branches 8 inches long & then the one from the base. It just looks odd but now is not the time to cut. Leaves are ok. Some fall off in winter but it is hard with central heating. Leaves on this plant are all ok