Does an increase in GDP result in a direct increase in production? For example, a 5% increase in GDP results in a 5% increase in production for a country?
Gross Domestic Product measures production in terms of value (usually "GDP" alone refers to GDP in real terms, while we add the qualifier "nominal GDP" to indicate that we use current prices).
As such an increase in GDP may not be accompanied by an increase in production as measured in quantity, if this is what the OP asks.
Even if we take out the effect of price inflation, we may have changes in what is produced, such that fewer units are produced but each of a higher value -higher enough so as the overall effect to be an increase in GDP (i.e. in value terms).
Think of a country that produced grain of a given quality. Next year it switches grain variety, and it now cultivates a variety that produces fewer tons of product but it is priced higher because it is considered more healthy.
Or think of car production, where we produce 1 million small cheap cars, and next year we switch to high-end cars. We may now produce a much lower quantity of cars, but each cars costs/is priced much more, and overall we may see an increase in the value of GDP (always speaking in real terms here). But if we want to count the number of end-product units, it has decreased.
GDP is a statistical indicator which is an estimate of production that has already occurred, or an estimate of the current or future level of production. The units are generally nominal, or adjusted by some variety of methods to correct for different changes in price levels across a changing production structure (e.g., more smartphones, less typewriters).
So I'm not sure if this involves confusion or disagreement about the precise meaning of "GDP", or a misunderstanding about the sequential order of logic. Specifically, the order in time is 1) production occurs, 2) there is a measurement indicator intended to reflect the production which actually occurred.
For an example of how this could be important, consider the following example. Production increases equally across all sectors by 5%. However, a change in price levels can differ from one sector to another. So using some methods the statistical indicator called "GDP" will increase by precisely the same 5%, and according to other methods of calculating GDP it could be different from 5%.
Conceptually, differences in these methods might be straightforward to understand in principle, but implementing the methods can become complicated, and there is liable to be some "art" in determining which method is most appropriate for measurement, or for the use of the statistical indicator called "GDP" depending on the specific application. For example, if exchange rates are very important, such as in trade analysis, "real GDP" could be less important for knowing the effects on the overall budget situation of the government or the cost of capital in the financial system.
An issue that one must consider is inflation. If an event occurs in a country, (a debt crisis for example) inflation could rise to that extent that in nominal terms GDP increases by 5%. We have seen this in Venezuela over there years where the nominal increase in GDP is irrelevant because it is mostly due to inflation. In that scenario, production in terms of the quantity of goods produced can drop due to input costs, but nominal GDP can rise due to a devaluation of the currency. So GDP does not have to increase as a result of production. But all things being equal, a higher production rate CAN correspond with a higher GDP. The quantity of goods sold leading to an increase in GDP.