As I understand it the term "hyperglycemia" is used in two different (and slightly confusing) ways:
When I had my medical in February (2017) just before the diabetes diagnosis, the doctor ordered a routine blood-glucose test and before getting the results, he had scribbled in his notes: "Rule out hyperglycemia. He [Grateful] had an HbA1c of 5.5% in 2009." It was my first "routine medical" since 2009 which is why the doctor had looked up my previous, very old, A1c. In this case, what my doctor meant by "hyperglycemia" was really just a fancy term for "diabetes." The doctor wanted to "rule out" hyperglycemia but ended up, unfortunately, confirming it!
"Hyperglycemia" is also used, rather more precisely, to indicate times when someone (either a diabetic person, or a non-diabetic person) has an episode of high blood sugar.
BTW I am using the American spelling of the term, slightly different to the British (there is an "a" missing).
What Is relationship between Hyperglycemia and Hba1c ?
If you have high average hyperglycemia, you will have a high HbA1c. If you are, over a period of about three months and on average, hyperglycemic, your HbA1c will be in the "diabetic" range.