What troubles me about this question is that I don't have insight into your definition of "slow" and direct observations of the developer themselves. While I do appreciate time and budget constraints, often expectations of what software development entails are at odds with these things.

In general, if progress feels slow it is likely because the development cycle is too big. Consider using an agile framework like Scrum or Kanban to manage how much work is taken on and when it will be reviewed (eg. every week or every two weeks). Also consider "sizing" the work items so that they can be completed (ie. coded, tested, deployed into production) every 1-2d. This provides a benefit of lightening the load while improving progress through a backlog and providing much more rapid feedback on whether you're building the right things.

Finally, set your expectations accordingly: Software development is all about wrestling with wicked problems using a tractable medium. You likely won't get everything you want for a certain date, but you can control getting the most valuable things done for the time and money invested.

Good luck!