Glasgow.

I am trying to trace a relative born Glasgow 1943.
A "Care Order" was issued in 1944 in Glasgow, Would I be able to access
this Order, if so, where would I find it and what exactly is a Care

Charles Ellson...

Unlikely unless you are the person concerned or his/her agent.

Order?

Charles Ellson...

[bearing in mind that the query concerns 1943-]
It is an order from the Sheriff Court which (in effect if not in
strict law) transfers responsibility for the child in whole or in part
from the parents to the local authority. In some cases the reasons
might be non-culpable if e.g. the parent(s) become incapable (possibly
only temporarily) of providing care due to their own illness or
poverty while in others it could be due to the negligence of the
parents/guardians. Depending on the circumstances, the child might
have remained at home (probably a minority of cases), been placed with
a relative or foster parents or in a home run by or on behalf of the
local authority.
It is also possible under current legislation for a child to be
committed into care due to having committed criminal offences but I am
not familiar with the actual legal mechanism by which this was
achieved 60 years ago.
Note that each jurisdiction in the UK has its own laws regarding these
matters so any description of similar procedures in England and Wales
(or Northern Ireland) could be a red herring.