If UK attacks and does not finish the standing army off, the standing army stays there.
I generally represent such a scenario with French units atop of chips as the French are the least utilized army.
If the Axis then moves in, you would represent all units there with the Axis nation that claims the remaining standing army. So in example:
UK attacks Turkey and has to retreat after killing 4 units.
Put 1 French Inf atop of the remaining units (3, I think?)
Italy then moves in and claims Turkey.
Remove the French INF, place an Italian INF atop the chips. They now move and act as Italian units.
Pretty sure that is how the scenario would work. Just remember that claiming neutral standing armies is part of the NCM phase, so those units in Turkey can only defend until the subsequent Italian turn.