You might be looking for the term monopsony power or perhaps oligopsony power.
A superficial look at the literature indicates that the Herfindahl-Hirschman index (HHI), so commonly used in assessing seller market power, is also used to measure buyer market power. Recall that the HHI is the sum of the squared market shares measured in percent (so a duopoly with two sellers of 10% and 90% market shares has an HHI of $90^2 + 10^2 = 8,200$.
If you have buyer level figures (not clear to me from your question) then your data allows you to construct local and aggregate buyer market shares. You'll have to convince yourself which is the right market share for understanding the relevant market. For example, if they were dry cleaners, they tend to draw resources from a small area, and each store is probably a distinct market. If they are car dealers, they draw customers from all over, and so perhaps the entire set of sales is the relevant market.
In the follow up comments and question, Hardy asks, "I want to see how the market power is exercised in terms of its effect on price." In general, you can't do this with price and quantity data alone because prices are simultaneously determined by supply and demand. Unless you know whether supply or demand or shifting, you can't know why prices are changing.
If you really knew that "an additional buyer comes into the market at a given location", and you knew something about what their demand schedule looked like, and you knew that their arrival was exogenous to changes in supply, then I think you could trace out the supply curve and learn about the supply elasticity (for example). But I think you generally need exogenous variation in supply to trace out the demand curve (and vice versa).
However, I'm concerned that the arrival of a purchasing customer is an equilibrium outcome (they only buy when they like the price) while the arrival of a potential customer is what actually is in the demand curve and influences the degree of monoposony. To see this starkly, recall that there are a number of competitive settings where even potential entrants can fully discipline a monopolist to provide the competitive price and ensure they earn zero profits. For example, Tirole Chapter 8. The monopsonist version probably works the same way: in the presence of free entry, if the monopsonist earns any rents then other buyers will enter until those rents are competed away. Therefore we cannot generally learn much just from observing the market quantities (what we really want is unobserved). This makes me skeptical that your data can identify what you are hoping to identify.
However, if you can argue, using your knowledge of the institutional setting, that the appearance of positive quantity purchasers are independent of pricing (they are movements of the demand curve and not movements along a demand curve), then I think you trace out the supply curve with your data. Then, you can look for something similar to the Monopsony and the Minimum Wage outcome. In that setting, the minimum wage raises price and quantity demanded. In yours, entry would lead to higher prices and higher quantities. Could you do that in your data? After deciding whatever is the exogenous shift in demand, can you look (perhaps in a regression difference in difference setting (diff 1: markets with and without such entry with the same change in quantity, diff 2: before and after entry) to see if prices go up along with quantities after entry?
