How to buy out time for new projects in case all resources are packed?

HI Prashant, If I'm reading your question right, you're asking - how do we get time from the developers who are working on billable projects to help scope out the 'to be' work? Developers shouldn't be 100% billable, the better guideline here is 80%, that leaves 20% free for vacation, training, meetings, and proposal support. If you've got resources booked to capacity, the organization is endangering the pipeline of future work.

some ways to buy time and to keep client calm for few days:

1. Involve customer in some decision making process like selection of framework, approach, testing strategies, environment setup, etc. Client would be engaged in some of the activities and would not focus on non-productivity
2. Create a prototype (if possible) by using some junior resources. Client usually get a sense of work accomplished when some Prototype is displayed
3. Add few resources and start the work. Convey to the client that more resources are expected in another 1-2 weeks
4. Identify re-usable components of historical projects and see if you can use it to quickly start the work with less number of resources

it is a dangerous situation if current projects are not closer to finish

There are some ways to buy an extra time, as Liana and Sonali says, check the resource calendars, check if you can adjust to reduce percent of some of your resource, but be carefull and keep on mind that project would be extensive in time too.
Search for tools to reduce time in current project to release resource as quick as you can
and think too in third party to help you

Hi Prashant,
If I understand correctly, you have a team that are assign to project 100% of their time. That is a dangerous situation by itself. Liane suggestion of 80% is very good.

Options is to stall the client, try to gather more clarification .... Hire more ressources to reach the 80% of billable time.

This is a case of priority management. There's only so many hours in a day and sometimes difficult choices need to be made. Have a clear agreed upon prioritized list with stakeholders and management and show how resources are being consumed against the projects.