Is there an app that allows me to monitor time spent using an application?

The application Time Sink ($5, Many Tricks) tracks the amount of time you spend in each application (and each window within an application).

Timing helps in tracking time spent in applications (and their windows) as well. It's similar to Time Sink but seems to provide more grouping and reporting options.

TimeEdition is an application that I just found. I haven't used it yet, but it's free. However, it doesn't have as many features as Time Sink.

macOS Catalina might bring Screen Time as in iOS to Mac too.

Usage reports Screen Time creates usage reports that show you how much time is being spent on your Mac, which apps are used most and how many notifications are received. With iCloud, Screen Time combines all your usage information and syncs Downtime settings and App Limits across iPhone, iPad and Mac.

Downtime With Screen Time: you can schedule downtime so you (or your child) can only use specific apps you’ve approved.

App Limits With App Limits you can set the amount of time you want to use your apps and websites. Set App Limits for total time, categories or specific apps.

Combined Limits Create combined limits with a combination of app categories, specific apps or websites.

One More Minute When a limit is met, you can tap “one more minute” to give you time to quickly save your work or wrap up a conversation.

emphasis and some punctuation mine.

https://www.apple.com/in/macos/catalina/features/