If your current Agile practices and approaches are:
Some projects are Agile where continuous feedback from client will be coming, and the developers need to work on the existing item if it's in testing phase too because the deadline of a project will be too short and the client won't extend the deadline.
Then you are not agile
Although Agile does indeed depend on fast and immediate feedback from the customer, if this is misapplied and turned into "continuous feedback from the client that needs to be applied immediately" - and this bypasses the agile development process - it does not 'make' you agile. In good agile shops you can take a concept from idea to production in minutes if you have spend the time up front architecting a well designed and tested system. This is where the rubber hits the road for all the good practices you can read about. They may sound good 'in theory' but to realize their touted benefits they have to actually be applied and that is hard.
Agile means that you develop software differently. This does not automatically mean high costs, expensive equipment or additional servers.
I recommend you focus on:
- Learning more about Agile Development
- Learn more about TDD
- Learn more about BDD
- Learn about Scrum
- Learn about Kanban
- Learn about Agile Testing Pyramid
- Learn about Agile Testing Quadrants
"the deadline of a project will be too short and the client won't extend the deadline." has been the challenge of developing software for the last 50 years. Your responsibility is to educate the client or their representative about what quality testing means. If they refuse to talk I recommend finding other clients. If you continue with this client and don't change the approach it will just get worse and worse as time goes by.
Another note on cost - you can and nowadays should - use cloud services for your environment and pay a few dollars a day - or even a few cents - for a test environment.